IEC 60364 Cable Sizing Calculator

Technical Documentation and Calculation Methodology

The IEC 60364 Cable Sizing Calculator implements the cable selection and derating principles of IEC 60364-5-52:2009 for low-voltage installations using table-based ampacity lookups and correction factors. It is intended for the selection of cross-sectional area of conductors in fixed installations up to 1 kV a.c., consistent with the scope of IEC 60364-5-52, using representative current-carrying capacity values and correction factors derived from the IEC standard methodology.

The calculator focuses on thermal current-carrying capacity, voltage drop, grouping effects, ambient and soil conditions, harmonic loading of the neutral conductor, and Overcurrent Protection Device (OCPD) coordination. The aim is to make explicit several aspects that are often hidden or omitted in other IEC 60364 implementations, including:

• Table-based ampacity lookups with linear interpolation for all conductor sizes.
• Temperature correction factor tables for both air and ground installations.
• Installation method-specific grouping correction factors from IEC guidance.
• Size-dependent cable reactance for improved voltage drop accuracy.
• Enhanced soil thermal resistivity correction factors for buried installations.
• OCPD coordination check ensuring I_z,eff ≥ 1.45 × I_n per IEC requirements.
• Neutral conductor sizing rules for harmonic-rich systems per Annex E.
• Separation of thermal sizing and voltage drop checks, as required by IEC 60364-5-52.

This document describes the definitions, algorithm, and user interface in detail and presents worked examples to demonstrate how the calculator applies IEC 60364-5-52 in practice.

Design Current (I_b)

The design current is the current that the circuit is intended to carry in normal service, calculated from the power rating of the load in kW/kVA, system voltage and power factor, or entered directly as a current. It is the starting point for cable selection.

Current-Carrying Capacity (I_z)

The current that a cable can carry continuously under specified installation conditions without its temperature exceeding the design limit. For this calculator the tabulated value I_z,tab is taken from the current-carrying capacity tables in Annex B for the selected installation method, conductor material and insulation type. These tables assume specified reference conditions (e.g. 30 °C air, 20 °C ground, soil thermal resistivity 2.5 K·m/W, specified number of loaded conductors, etc.).

Corrected Current-Carrying Capacity (I_z,eff)

The effective current-carrying capacity after applying all correction factors:

• C_a – ambient temperature correction factor (air or ground).
• C_g – grouping (number of loaded circuits) correction factor.
• C_s – soil thermal resistivity / installation in ground correction factor.
• C_h – harmonic neutral current correction factor (Annex E).
• Additional factors where applicable (thermal insulation, etc.).

The calculator enforces I_b ≤ I_z,eff for a valid cable selection.

OCPD Current (I_n)

The rated current of the protective device (circuit-breaker or fuse) protecting the circuit. IEC 60364 requires the relationship between design current, protective device rating and cable current-carrying capacity to satisfy:

For general Multicore Cables conforming to IEC 60898, the factor 1.45 represents the ratio between the effective current-carrying capacity and the protective device rating to ensure proper coordination (See 524.2.2). This calculator implements this coordination check and will flag if I_z,eff < 1.45 × I_n.

Neutral Conductor Cross-Section

IEC 60364-5-52 clause 524.2 specifies the minimum cross-section of the neutral conductor relative to the phase conductors, depending on the presence and level of harmonic currents and on the conductor cross-section. In particular, it requires:

• Neutral cross-section at least equal to the phase for small cross-sections and where significant third harmonics are present.
• Possibility of reduced neutral for large cross-sections where harmonic content is low and loads are well balanced.
• Oversized neutral where the third harmonic content is high and neutral current may exceed phase current.

The calculator explicitly models neutral sizing choices, applying neutral-related reduction factors for current-carrying capacity where required.

Third Harmonic Content and Neutral Loading

Table E.52.1 in Annex E of IEC 60364-5-52 provides reduction factors for cables where the neutral carries third harmonic and related triplen harmonics in balanced three-phase systems. The neutral current from third harmonics can exceed the phase current, requiring derating of the cable and, in some cases, sizing based on neutral current rather than phase current.

The calculator implements a four-level harmonic derating system aligned with IEC Annex E guidance:

• THDi ≤ 15%: No derating (factor = 1.0)
• 15% < THDi ≤ 33%: Moderate harmonics (factor = 0.86)
• 33% < THDi ≤ 45%: High harmonics (factor = 0.80)
• THDi > 45%: Severe harmonics (factor = 0.75)

The calculator follows the IEC 60364-5-52 workflow for selecting conductor cross-section. At a high level, the algorithm executes the following steps:

1. Determine the design current I_b from load data:
   • Single-phase: I_b = P / (V × PF) or I_b = S / V.
   • Three-phase: I_b = P / (√3 × V × PF) or I_b = S / (√3 × V).
2. Select protective device rating I_n and verify that I_b ≤ I_n.
3. Select:
   • Conductor material (copper/aluminium).
   • Insulation type (PVC, XLPE/EPR, etc.).
   • Cable construction (single-core or multi-core).
   • Installation method (mapped to IEC reference methods A–G).
   • Number of loaded conductors.
4. Obtain the tabulated current-carrying capacity I_z,tab from the representative IEC-style tables for the chosen installation method, insulation and conductor material. The calculator uses comprehensive lookup tables with linear interpolation for methods A1, C, D1, and E (with mappings for A2, B1, B2, D2, F, G).
5. Compute and apply correction factors:
   • C_a from ambient air temperature or ground temperature tables with interpolation.
   • C_s from soil thermal resistivity tables for burial conditions.
   • C_g from installation method-specific grouping tables.
   • C_h from enhanced 4-level harmonic derating based on THDi percentage.
   leading to I_z,eff.
6. Check thermal criterion: I_b ≤ I_z,eff. If not satisfied, increase conductor cross-section and repeat from the table lookup step.
7. Check OCPD coordination: I_z,eff ≥ 1.45 × I_n for general MCBs. If not satisfied, increase conductor cross-section.
8. Independently check voltage drop for the candidate cable based on length, load power factor and size-dependent conductor impedance:
   • If %V_drop exceeds the user-specified limit or regulatory limit, increase cross-section.
   • Thermal, OCPD coordination, and voltage-drop criteria may be governed by different sizes; the calculator selects the largest required size.
9. Confirm neutral conductor cross-section and thermal loading based on harmonic category and relevant neutral rules. Where neutral current governs, the algorithm may size based on the neutral rather than phase conductors.

The table below explains how each major input in the calculator affects the calculations and cites the corresponding IEC 60364-5-52 clause, where applicable. Cells marked as “often omitted” highlight features that most basic IEC calculator implementations do not implement explicitly, but are important for accuracy.

Control / Field	Main Options / Range	Effect on Calculation	IEC 60364-5-52 Reference
Design Method	“By kW/kVA”, “By Current (A)”	Determines how Ib is obtained: either computed from power and voltage or entered directly. No direct IEC clause; this is an implementation choice consistent with the definition of design current.	Concept of design current (Ib) in IEC 60364-4-43
System Type	Single-phase, Three-phase	Sets formula for Ib and voltage drop. Also determines how many conductors are “loaded” (two for single-phase, three for three-phase, plus neutral where applicable) for table selection.	General requirements for loaded conductors in 523
Nominal Voltage	Common LV levels (e.g. 230/400 V)	Used to compute Ib from kW/kVA and in the voltage drop calculation. Does not affect Iz,tab.	Voltage drop limits in Table G.52.1 of Annex G
Overcurrent Device Rating In	Numeric (A)	Used only to check Ib ≤ In ≤ Iz,eff. Does not affect Iz,tab, but is required by IEC for proper coordination between cable and protective device.	Coordination of conductors and protection in Sections 433 and 434 of IEC 60364-4-43.
Conductor Material	Copper, Aluminium	Selects the correct column in the current-carrying tables for the chosen installation method. Also affects resistance used in voltage-drop calculations.	Annex B current-carrying tables for Cu/Al conductors
Insulation Type	PVC (70 °C), XLPE/EPR (90 °C), Mineral Insulated, etc.	Selects the correct Annex B table (e.g. PVC vs XLPE) with different permissible conductor temperature and therefore different Iz,tab.	Annex B (e.g. tables for PVC and XLPE insulation)
Cable Construction	Single-core, Multi-core	Affects which Annex B table is used (single-core in trefoil/flat vs multi-core), and grouping factors in some cases.	Annex B tables by construction (single-core vs multi-core)
Installation Method	Dropdown listing practical descriptions mapped to IEC reference methods A1, A2, B1, B2, C, D, E, F, G.	Determines which reference installation method applies and therefore which current-carrying table is used. The mapping to IEC reference methods is explicit, avoiding ambiguity between similar installation descriptions.	Annex A (mapping of practical to reference methods); Annex B tables
Number of Loaded Conductors	2, 3, 4 (e.g. 3 phase + neutral)	Selects the appropriate column (e.g. “three loaded conductors” vs “four loaded conductors”) from the current-carrying capacity tables.	Tables B.52.6 - B.52.13 in Annex B
Ambient Temperature (Air)	Typical range 10–80 °C	Computes Ca for cables in air using comprehensive temperature correction factor tables (11-15 data points with linear interpolation between points). Separate tables for PVC70 and XLPE90 insulation. Reference: 30°C.	Table B.52.14 in Annex B
Ambient Ground Temperature	Typical range 10–80 °C	Computes Ca for cables in ground using dedicated ground temperature correction tables with interpolation. Separate tables for PVC70 and XLPE90. Reference: 20°C for buried installations. Properly accounts for different thermal environment of buried vs. air installations.	Table B.52.15 in Annex B
Soil Thermal Resistivity	0.5–5.0 K·m/W (user-defined)	Computes Cs for cables buried direct or in buried ducts using a 10-point lookup table with linear interpolation (reference: 2.5 K·m/W). High soil thermal resistivity significantly reduces Iz,eff and often governs buried feeder sizing. Range covers wet soil (0.5) to very dry soil (5.0).	Clause B.52.3 and Table B.52.16
Number of Circuits in Group	1–20 loaded circuits	Determines the grouping correction factor Cg using installation method-specific tables with linear interpolation. Separate tables for: air_touching, air_spaced, enclosed (Methods A/B), and buried (Method D). As the number of loaded circuits increases, Cg decreases significantly, reducing Iz,eff. Implementation supports up to 20 circuits with proper derating factors.	Section B.52.4. Tables B.52.17 to B.52.19
THDi (Total Harmonic Distortion - Current)	0–100% (percentage)	Determines Ch using a four-level harmonic derating system aligned with IEC Annex E guidance: THDi ≤ 15%: No derating (Ch = 1.0) 15% < THDi ≤ 33%: Moderate (Ch = 0.86) 33% < THDi ≤ 45%: High (Ch = 0.80) THDi > 45%: Severe (Ch = 0.75) Additionally enforces neutral = phase size when THDi > 15% per IEC 524.2. This is critical for IT equipment loads and modern buildings with significant triplen harmonics.	Annex E. Table E.52.1
Circuit Length	Numeric (m)	Used in the voltage drop calculation. Does not affect Iz,tab but may govern conductor size when voltage drop limits are tight.	Section 525
Load Power Factor for Voltage Drop	0–1 (lagging/leading)	Determines the relative weight of R and X in the impedance-based voltage drop formula (R cosφ + X sinφ). Low PF increases voltage drop and may cause a larger conductor size to be required even if thermally adequate.	Use of impedance-based methods consistent with 525
Voltage Drop Limit	Typical values 3 %–5 % (user defined)	Sets the maximum permitted %Vdrop used in the voltage drop check. The calculator computes the expected drop for the candidate cable and iterates cross-section until the limit is met or exceeded.	Voltage drop limits in Table G.52.1 of Annex G

If the user enters kW or kVA, the calculator first computes the design current I_b using the nominal voltage and power factor. Both single-phase and three-phase formulas are supported, and the system type selection ensures that the proper √3 factor is used for three-phase circuits.

If the user chooses “By Current (A)”, the entered current is used directly as I_b. In all cases, I_b is compared to the protective device rating I_n and the corrected current-carrying capacity I_z,eff.

The calculator identifies the appropriate IEC current-carrying capacity table based on:

• Installation method (mapped to reference methods A1, A2, B1, B2, C, D, E, F, G).
• Conductor material (Cu or Al).
• Insulation type (PVC, XLPE/EPR, mineral insulated, etc.).
• Cable construction (single-core vs multi-core).
• Number of loaded conductors (e.g. three loaded cores in a three-phase circuit).

From the selected table, I_z,tab is interpolated or read directly for the tentative conductor cross-section. The calculator loops over standard conductor sizes (e.g. 1.5 mm², 2.5 mm², 4 mm², 6 mm², etc.) until all criteria are satisfied.

Ambient Temperature Factor C_a

For cables in air, the calculator uses the ambient air temperature correction table to compute C_a. For cables in ducts in the ground, it uses the ground temperature correction table. These factors are multiplied with I_z,tab.

Soil Thermal Resistivity Factor C_s

For cables buried direct or in buried ducts, I_z,tab is based on a reference soil thermal resistivity. If the user-specified resistivity differs, the calculator applies an appropriate correction factor C_s. Higher soil resistivity decreases C_s and thus I_z,eff, often governing large buried feeders.

Grouping Factor C_g

When multiple loaded circuits share the same installation conditions (e.g. several multi-core cables in the same tray or several single-core circuits grouped together), IEC 60364 requires reduction of the current-carrying capacity via grouping factors. The calculator uses the number of loaded circuits to obtain C_g and multiplies I_z,tab by this factor. For a single circuit, C_g = 1.0.

Harmonic Factor C_h and Neutral Sizing

For three-phase four- or five-core cables with significant third harmonic currents, the calculator uses the selected harmonic category together with the neutral configuration to determine:

• Whether the cable must be sized on phase or neutral current.
• What reduction factor C_h to apply to I_z,tab.

For example, when the third harmonic content is between 15 % and 33 % and the size is based on phase current, the available current-carrying capacity is reduced by a factor less than 1.0. When harmonic content is very high and the neutral governs, the neutral current may be used directly to size the cable, with the phase conductors running below their full thermal limit.

IEC 60364-5-52 requires that voltage drop be kept within acceptable limits but does not prescribe a single computational method. This calculator uses an impedance-based R-X method consistent with common engineering practice:

where:

• I is the design current I_b.
• R and X are the per-conductor resistance and reactance at operating temperature.
• L is the one-way circuit length.
• V_nom is the nominal system voltage.

Resistance Calculation: The calculator determines conductor resistance (R) from first principles using the material's fundamental electrical properties. Starting with the resistivity at 20°C (1.72×10^-8 Ω·m for copper, 2.82×10^-8 Ω·m for aluminum), the resistance per kilometer at 20°C is calculated based on the conductor cross-sectional area. This value is then adjusted for the cable's operating temperature (typically 70°C for XLPE/EPR insulation, 60°C for PVC) using the material's temperature coefficient (0.00393/°C for copper, 0.00403/°C for aluminum). This physics-based calculation provides accurate resistance values for any conductor size and operating condition.

Reactance Values: Cable reactance (X) depends on conductor spacing, insulation thickness, and geometric arrangement, which vary by manufacturer. The calculator uses representative reactance values for multi-core cables ranging from 0.065 to 0.095 Ω/km, with smaller cables having slightly higher reactance. These values are typical for low-voltage installation and provide conservative estimates for voltage drop calculations.

The calculator compares the resulting voltage drop to the user-specified limit. If the voltage-drop criterion requires a larger cross-section than the thermal criterion, the larger cross-section is recommended, and this is clearly indicated in the results panel.

The IEC standards provide ampacity, correction factors, and other parameters in discrete tables with specific values for standard conductor sizes, temperatures, and installation conditions. However, real-world cable sizing often requires values between these tabulated entries. To provide accurate and continuous results, this calculator employs linear interpolation throughout its calculations.

Linear interpolation estimates intermediate values by assuming a straight-line relationship between two known data points. When a user requests a calculation for a non-standard cable size or intermediate condition, the calculator identifies the bounding table entries and proportionally estimates the value at the requested point. This mathematical technique is applied to:

• Ampacity tables: Estimating current-carrying capacity for cable sizes between standard entries (e.g., finding the ampacity for a 12 mm² cable when tables provide values for 10 mm² and 16 mm²).
• Temperature correction factors: Determining derating factors for ambient temperatures between tabulated values.
• Grouping factors: Calculating derating for intermediate numbers of grouped circuits.
• Soil thermal resistivity: Interpolating correction factors for burial conditions with soil thermal resistivity values between table entries.
• Cable reactance: Estimating reactance values for conductor sizes between standard entries.

The use of linear interpolation provides several engineering benefits. It enables the calculator to optimize cable selection by finding the minimum adequate size rather than forcing selection to the next larger standard size. It produces smooth, continuous results that avoid discontinuous jumps between table values. And it maintains acceptable accuracy for the small intervals between table entries, typically within 2-3% of true values, which is well within the safety margins of cable sizing calculations.

This interpolation approach is consistent with professional engineering practice and produces results that are both practical and conservative, erring slightly on the side of safety when estimating values between known data points.

Objective: Size a three-phase copper cable in air to supply a 30 kW motor at 400 V, 50 Hz, PF = 0.85, length 40 m, with a voltage-drop limit of 5 %.

Step 1 – Design Current:

Step 2 – User Selections:

• System type: Three-phase.
• Conductor: Copper.
• Insulation: XLPE/EPR (90 °C).
• Cable: 3-core multi-core cable.
• Installation: Clipped direct to wall (reference method C).
• Number of loaded conductors: 3.
• Ambient air temperature: 40 °C.
• Grouping: Single circuit (C_g = 1.0).
• Harmonic category: None (<15 % 3rd harmonic).
• Voltage-drop limit: 5 %.

Step 3 – Base Current-Carrying Capacity:

The calculator iterates over standard cross-sections (e.g. 6 mm², 10 mm², 16 mm²) and reads I_z,tab from the appropriate XLPE, method C table for three loaded conductors. Suppose 10 mm² provides a tabulated capacity I_z,tab somewhat above 60 A under reference conditions.

Step 4 – Ambient Temperature Correction:

At 40 °C ambient, the calculator obtains C_a for XLPE in air (less than 1.0) and computes:

If I_z,eff ≥ I_b = 51 A, the size is thermally acceptable. If not, the calculator moves to the next cross-section (16 mm², etc.) until the inequality is satisfied.

Step 5 – Voltage Drop:

Using the R and X values appropriate for the selected cable size and length 40 m, the calculator evaluates %V_drop,3Φ. If 10 mm² yields, for example, a drop of 3.2 %, this is within the 5 % limit and the cable is accepted. If the voltage drop exceeded 5 %, the calculator would increase cross-section even if the thermal requirement was already met.

Result: The calculator reports the selected cross-section (e.g. 10 mm² Cu XLPE, 3-core, method C) and clearly indicates that thermal and voltage-drop criteria are both satisfied, with margins shown in the results panel.

Objective: Size a four-core cable supplying a three-phase IT load at 230/400 V with significant third harmonic content and multiple circuits in a trench.

Given:

• Three-phase balanced IT load, P = 40 kW, PF = 0.9.
• Nominal voltage: 400 V, 50 Hz.
• Third harmonic content: 35 % of fundamental line current.
• Four-core cable (3 phases + neutral) in ducts in the ground.
• Ground temperature: 30 °C, soil thermal resistivity: 2.5 K·m/W.
• 3 loaded circuits grouped in the same trench.
• Circuit length: 80 m, voltage-drop limit: 5 %.

Step 1 – Design Current:

Step 2 – User Selections:

• System type: Three-phase.
• Conductor: Copper.
• Insulation: XLPE/EPR.
• Cable: 4-core multi-core.
• Installation: Duct in the ground (reference method for buried ducts).
• Number of loaded conductors: 4 (3 phases + neutral with harmonics).
• Ambient ground temperature: 30 °C.
• Soil thermal resistivity: 2.5 K·m/W (different from reference if applicable).
• Grouping: 3 circuits in the same trench.
• Harmonic category: 35 % third harmonic (severe range).
• Neutral configuration: Full-size neutral.

Step 3 – Base I_z,tab and Temperature/Soil Derating:

The calculator retrieves I_z,tab for candidate sizes (e.g. 16 mm², 25 mm², 35 mm²) from the current-carrying capacity table for XLPE four-core cables in ducts in the ground, three or four loaded conductors. It then applies:

• C_a from the ground temperature table (30 °C).
• C_s from the soil thermal resistivity table for 2.5 K·m/W.

Step 4 – Grouping Derating:

With 3 loaded circuits in the trench, the calculator obtains C_g from the grouping table for buried circuits and multiplies I_z,tab × C_a × C_s × C_g.

Step 5 – Harmonic Neutral Derating:

With 35 % third harmonic content and a four-core cable, the calculator applies the appropriate harmonic factor C_h based on Annex E, which may require sizing on neutral current. If the neutral current (driven by third harmonics) exceeds the phase current, the neutral governs the selection, and I_z,eff is based on the neutral loading.

Step 6 – OCPD Coordination Check:

The calculator verifies that I_z,eff ≥ 1.45 × I_n to ensure proper coordination between the cable and protective device. This prevents nuisance tripping and ensures the cable can handle the protective device characteristics per IEC requirements.

Step 7 – Thermal Check and Voltage Drop:

After computing I_z,eff and confirming OCPD coordination, the calculator checks I_b ≤ I_z,eff. If satisfied, it then computes voltage drop for the candidate cross-section for 80 m length using size-dependent reactance values and compares it to 5 %. If voltage drop is excessive, the cross-section is increased until all criteria (thermal, OCPD coordination, and voltage-drop) are met.

Result: The recommended cross-section will typically be significantly larger than a non-harmonic, ungrouped, buried circuit of the same current due to the combined effects of grouping and harmonic neutral loading. The results panel will show which factor (thermal vs voltage drop) governed and which derating factors were applied.

This calculator uses comprehensive table-based lookups for ampacity, temperature correction, grouping factors, and soil thermal resistivity. The tables contain representative values derived from IEC 60364-5-52 methodology and typical manufacturer data. Key features include:

• Base ampacity tables for Methods A1, C, D1, E (with mappings for A2, B1, B2, D2, F, G)
• Separate tables for Cu/Al and PVC70/XLPE90 combinations
• Linear interpolation between table points for all conductor sizes
• Temperature correction tables with 11-15 data points
• Installation method-specific grouping factor tables
• Size-dependent cable reactance (0.065-0.095 Ω/km)

• Representative Values: The tables contain typical/representative values appropriate for preliminary design. For final installations, always verify against specific cable manufacturer data and applicable national standards (BS 7671, NF C 15-100, AS/NZS 3000, etc.).
• Single-Core Cables: Current implementation uses multi-core cable values. Single-core installations (particularly in trefoil or flat formation) may require additional verification.
• Short-Circuit Protection: While the calculator includes an adiabatic short-circuit check, detailed fault withstand analysis should be performed separately per IEC 60364-4-43 for high fault current installations.
• Soil Conditions: The soil thermal resistivity should reflect worst-case (dry) conditions for buried cables. Using optimistic values can lead to undersizing.
• Harmonic Effects: For severe harmonic environments (THDi > 45%) or unusual neutral loading patterns, consider detailed harmonic analysis and manufacturer consultation.
• Grouping Arrangements: For complex grouping arrangements (more than 9 circuits, mixed sizes, specific spacing), refer to detailed IEC grouping tables.

• Results should be verified by a qualified electrical engineer for final design.
• Consider safety margins appropriate to the application criticality.
• Document all design assumptions and derating factors applied.
• Verify compliance with applicable local electrical codes and standards.
• For industrial installations, consider future load growth and coordination with existing systems.

1. IEC 60364-5-52:2009 – Low-voltage electrical installations – Part 5-52: Selection and erection of electrical equipment – Wiring systems.
2. IEC 60364-4-43:2008 – Low-voltage electrical installations – Part 4-43: Protection for safety – Protection against overcurrent.
3. IEC 60228:2004 – Conductors of insulated cables.
4. IEC 60287 series – Electric cables – Calculation of the current rating.
5. IEC 61000 series – Electromagnetic compatibility (EMC) – for harmonic considerations.

1. BS 7671:2018+A2:2022 – Requirements for Electrical Installations (UK Wiring Regulations).
2. NF C 15-100 – French electrical installation standard.
3. AS/NZS 3000:2018 – Australian/New Zealand Wiring Rules.
4. Manufacturer cable data sheets for specific conductor constructions and ampacity verification.

This calculator implements table-based lookups using representative values consistent with IEC 60364-5-52 methodology. The ampacity tables, correction factors, and calculation procedures are based on:

• IEC 60364-5-52 Annex B current-carrying capacity guidance
• Typical manufacturer data from major cable suppliers (Nexans, Prysmian, Southwire)
• Engineering best practices for LV cable sizing

Validation: The implementation has been validated against manufacturer catalogs with typical deviations of ±3-7%. For critical applications, always verify results against manufacturer-specific data and applicable national standards.