Arc Flash Calculator

Technical Documentation and Calculation Methodology

The Arc Flash Calculator uses the complete IEEE 1584-2018 model, the latest industry standard for assessing arc flash risk. The 2018 edition represents a major revision over the older 2002 version. It incorporates new research, covers a wider range of voltages, and improves accuracy with specific calibration constants for different system voltages. The calculator handles everything from the initial arcing current, incident energy, and arc flash boundary, right down to applying the correct enclosure correction factors.

Per IEEE 1584-2018, the calculation methodology is applicable within the following ranges:

Enclosure dimensions affect the Correction Factor (CF) calculated per Equations (14) and (15). These inputs are only active for enclosed electrode configurations (VCB, VCBB, HCB). For open air configurations (VOA, HOA), CF is automatically set to 1.0 and these fields are disabled.

The Correction Factor (CF) modifies incident energy and arc flash boundary calculations based on enclosure size. The calculation follows IEEE 1584-2018 Equations 13, 14, and 15:

The equivalent height and width may require transformation from actual dimensions using Equations 11 and 12 depending on the electrode configuration and voltage range. For most applications, Height₁ and Width₁ equal the actual enclosure dimensions converted to inches.

Critical difference: Equation 15 for shallow enclosures uses the reciprocal of the polynomial, not the polynomial directly. This is a key implementation detail that affects calculation accuracy.

Where b1, b2, and b3 coefficients depend on:

• Electrode configuration: VCB, VCBB, or HCB (VOA/HOA always use CF = 1.0)
• Enclosure classification: "Typical" (Equation 14) or "Shallow" (Equation 15)

Shallow Enclosure Criteria (all must be met):

• System voltage < 600V
• Depth ≤ 203.2 mm (8 inches)
• Height < 508 mm (20 inches)
• Width < 508 mm (20 inches)

Example CF Coefficients from Table 7:

Physical Interpretation: Larger enclosures (higher EES) generally increase CF above 1.0, which reduces the calculated incident energy by reducing the energy concentration at the worker location. Smaller enclosures concentrate energy and may result in CF < 1.0 (though rarely below 0.4). The reciprocal formula for shallow enclosures (Equation 15) accounts for different arc behavior in very small, shallow boxes where pressure relief is limited.

The calculator performs calculations in the following sequence per IEEE 1584-2018:

1. Calculate arcing current I_arc at 600V, 2700V, and 14300V anchor points (Equation 1)
2. Interpolate arcing current for actual system voltage (Section 4.2.2)
3. Calculate reduced arcing current I_arc-min using variation correction factor (Equation 2)
4. Calculate correction factor CF based on enclosure geometry (Table 7, Section 4.8)
5. Calculate incident energy at both I_arc and I_arc-min (Equations 3-24)
6. Use maximum incident energy for final results (Section 4.5)
7. Calculate arc flash boundary distance (Equations 3-24 with D as unknown)
8. Determine PPE category based on incident energy (NFPA 70E Table 130.5(G))

Arcing current is calculated using Equation 1 from IEEE 1584-2018:

Where:

• I_{arc_Voc} = Arcing current at the specified V_oc (kA)
• I_bf = Bolted fault current for three-phase faults (symmetrical rms) (kA)
• G = Conductor gap (mm)
• V_oc = Open-circuit voltage (kV) - determines which coefficient table to use
• k1 through k10 = Electrode configuration-specific and voltage-specific coefficients from Table 1
• lg = logarithm base 10 (log₁₀)

The arcing currents are calculated at three different open-circuit voltage levels (600V, 2700V, 14300V). The calculator performs this calculation at all three voltage anchor points using the appropriate coefficient sets from Table 1, then interpolates for intermediate voltages using Equations 16-18.

For system voltages between anchor points, the calculator uses three-segment interpolation per IEEE 1584-2018 Equations 16-18:

Note: V_oc must be in kilovolts (kV) for these equations. The interpolation uses reference voltages of 0.6 kV, 2.7 kV, and 14.3 kV with scaling factors of 2.1 and 11.6 derived from the voltage differences.

For voltages below 600V (including 208V, 240V, 480V), IEEE 1584-2018 provides Equation 25 for improved accuracy:

This correction accounts for the non-linear relationship between voltage and arcing current at low voltages. The equation ensures that as voltage decreases below 600V, the arcing current reduces appropriately relative to the bolted fault current.

IEEE 1584-2018 requires calculation of a reduced arcing current to account for arc instability and variation. The variation correction factor (VarC_f) is calculated using Equation 2:

The reduced arcing current is then calculated as:

Typical VarC_f values range from 0.15 to 0.25, meaning I_{arc_min} is approximately 87-93% of I_arc (reduced by 7-13%). The coefficients k1-k7 are electrode configuration-specific and provided in Table 2 of IEEE 1584-2018.

Incident energy is calculated using Equations 3-6 from IEEE 1584-2018. The general form at each voltage anchor is:

Where:

• E = Incident energy at the voltage anchor (J/cm²)
• T = Arc duration (milliseconds)
• G = Conductor gap (mm)
• D = Working distance (mm)
• I_bf = Bolted fault current (kA)
• I_arc = Arcing current at the specific voltage anchor (kA)
• CF = Correction factor from Equations 14/15 and Table 7
• k1 through k13 = Voltage-specific and electrode configuration-specific coefficients from Tables 3, 4, 5
• lg = logarithm base 10 (log₁₀)

The result in J/cm² is converted to cal/cm² by dividing by 4.184 (1 cal = 4.184 J).

Equations 3, 4, 5, 6 correspond to:

• Equation (3): E₆₀₀ - Incident energy at 600V using Table 3 coefficients
• Equation (4): E₂₇₀₀ - Incident energy at 2700V using Table 4 coefficients
• Equation (5): E₁₄₃₀₀ - Incident energy at 14300V using Table 5 coefficients
• Equation (6): E_≤600 - Incident energy for V_oc ≤ 600V using Table 3 coefficients with I_arc from Equation 25

The calculator performs this calculation at both I_arc with T_arc and I_{arc_min} with T_{arc_min}, then uses the maximum value as the final incident energy.

For system voltages between the anchor points (600V, 2700V, 14300V), the final incident energy is determined using three-segment interpolation identical in structure to the arcing current interpolation:

Where E₆₀₀, E₂₇₀₀, and E₁₄₃₀₀ are the incident energies calculated at each voltage anchor using Equations 3, 4, and 5 respectively. V_oc must be in kilovolts for these interpolation equations.

The arc flash boundary (AFB) is calculated by solving the incident energy equation for distance D, setting E equal to the incident energy threshold (typically 1.2 cal/cm²):

Where:

• AFB = Arc flash boundary distance (mm)
• T = Arc duration (milliseconds)
• The constant 20 represents the incident energy threshold: 20 cal/cm² = 1.2 × 4.184 J/cm² × 4.184
• All other parameters and coefficients are the same as in the incident energy equations

Equations 7, 8, 9, 10 correspond to:

• Equation (7): AFB₆₀₀ - Arc flash boundary at 600V
• Equation (8): AFB₂₇₀₀ - Arc flash boundary at 2700V
• Equation (9): AFB₁₄₃₀₀ - Arc flash boundary at 14300V
• Equation (10): AFB_≤600 - Arc flash boundary for V_oc ≤ 600V

This calculation is also performed at both I_arc and I_{arc_min}, with the maximum distance used as the arc flash boundary.

For system voltages between the anchor points, the final arc flash boundary is determined using three-segment interpolation:

The interpolation methodology for arc flash boundary is identical to that used for arcing current and incident energy, ensuring consistency across all calculations.

The calculator maps calculated incident energy to PPE categories per NFPA 70E Table 130.5(G):

This calculator implements the complete IEEE 1584-2018 methodology with careful attention to the standard's specific requirements and equations. The following subsections detail the key aspects of the implementation.

The calculator implements the full IEEE 1584-2018 voltage interpolation methodology with calculation at three anchor points (600V, 2700V, 14300V) using three-segment interpolation between anchors per Equations 16-18, 19-21, and 22-24. Each anchor point uses distinct coefficient sets for arcing current and incident energy calculations as specified in Tables 1-5 of the standard.

This three-segment interpolation methodology ensures accurate results across the entire voltage range from 208V to 15kV, with particular attention to the transition regions between voltage anchors where simple linear interpolation would introduce significant errors.

The calculator uses the time base value of 50 ms as explicitly specified in IEEE 1584-2018 Equations 3-6. The standard shows the term (12.552/50) × T in the incident energy equations, where T is the arc duration in milliseconds. This time scaling factor of T/50 is a fundamental constant in the IEEE 1584-2018 incident energy model.

Important: The time base constant of 50 milliseconds is unambiguously specified in the standard equations and must be implemented correctly. Using an incorrect value would cause incident energy and arc flash boundary results to be drastically wrong—for example, using 0.5 instead of 50 would cause incident energy results to be 100× too high.

The calculator always calculates incident energy at both nominal arcing current (I_arc) and reduced arcing current (I_{arc_min}) with their respective clearing times, then uses the maximum value as the final result. This follows the IEEE 1584-2018 requirement to evaluate worst-case scenarios where reduced current may result in longer clearing times.

The reduced arcing current accounts for arc instability and variation, and is calculated using Equation 2 with the variation correction factor (VarC_f). When the protective device has an inverse-time characteristic, the reduced current scenario can produce higher incident energy than the nominal current scenario despite the lower current magnitude.

The calculator distinguishes between "Typical" and "Shallow" enclosures using the complete criteria specified in IEEE 1584-2018 (voltage < 600V, depth ≤ 203.2mm, height < 508mm, width < 508mm) and applies the appropriate coefficient sets from Table 7.

Critical Implementation Detail: The correction factor for shallow enclosures uses Equation 15, which applies the reciprocal of the polynomial (CF = 1 / [b1×EES² + b2×EES + b3]), not the direct polynomial used for typical enclosures (Equation 14). This reciprocal formula accounts for different arc behavior in very small, shallow boxes where pressure relief is limited.

The calculator implements Equation 25 for improved accuracy at voltages below 600V (208V, 240V, 480V, 600V). This equation accounts for the non-linear relationship between voltage and arcing current at low voltages, providing more accurate results than simple voltage interpolation alone.

Equation 25 is applied whenever the system voltage is at or below 600V, and uses the arcing current calculated at the 600V anchor point (I_{arc_600}) along with the bolted fault current to determine the final arcing current at the actual system voltage.

A key feature of IEEE 1584-2018 is the three-segment interpolation methodology used for arcing current (Equations 16-18), incident energy (Equations 19-21), and arc flash boundary (Equations 22-24). This methodology calculates values at three voltage anchor points (600V, 2700V, 14300V), then uses a sophisticated blending approach for intermediate voltages.

For voltages between 0.6 kV and 2.7 kV: The interpolation calculates two intermediate terms (one based on the 600V-2700V range, another based on the 2700V-14300V range), then blends them using weighted factors that vary with voltage. This ensures smooth transitions and accurate results across the voltage spectrum.

For voltages above 2.7 kV: The interpolation uses the 2700V-14300V range with the reference voltage of 14.3 kV, providing accurate scaling for medium-voltage applications up to 15 kV.

The calculator performs comprehensive validation of all inputs against IEEE 1584-2018 applicability limits:

The following examples demonstrate complete arc flash calculations using the calculator for typical electrical system configurations. All examples follow IEEE 1584-2018 methodology and show intermediate calculation steps.

Scenario

A 480V motor control center (MCC) with typical construction and protective devices. This is a common industrial electrical configuration requiring arc flash hazard analysis per NFPA 70E.

Given:

• System Voltage: 480V (three-phase, line-to-line)
• Bolted Fault Current: 35 kA (from short circuit study)
• Equipment Type: MCC
• Electrode Configuration: VCB (Vertical conductors in box)
• Conductor Gap: 25 mm (typical for 480V MCC)
• Enclosure Height: 508 mm
• Enclosure Width: 508 mm
• Enclosure Depth: 508 mm
• Working Distance: 457 mm (18 inches, typical for MCC)
• Clearing Time at I_arc: 100 ms (from TCC at ~25 kA)
• Clearing Time at I_arc-min: 150 ms (from TCC at ~21 kA)
• Incident Energy Threshold: 1.2 cal/cm²

Step 1: Calculate Arcing Current

For 480V (below 600V), use Equation 1 at 600V anchor point with VCB coefficients:

Iteratively solving Equation 1:

Apply Equation 25 for voltage below 600V:

Step 2: Calculate Reduced Arcing Current

Using variation correction factor coefficients for VCB from Equation 2:

Step 3: Calculate Correction Factor

Enclosure classification: V_oc = 480V < 600V, but H = 508mm ≥ 508mm, so classification is Typical (not Shallow).

Step 4: Calculate Incident Energy at I_arc

Using Equations 3-24 with VCB 600V coefficients:

Step 5: Calculate Incident Energy at I_arc-min

Using I_arc-min = 21.6 kA, T = 150 ms:

Step 6: Determine Final Incident Energy

The reduced arcing current scenario produces higher incident energy due to the longer clearing time (150 ms vs 100 ms), demonstrating the importance of checking both scenarios per IEEE 1584-2018.

Step 7: Calculate Arc Flash Boundary

Solving for distance D where IE = 1.2 cal/cm² (threshold):

The arc flash boundary is well inside the working distance, indicating relatively low arc flash hazard at this location.

Step 8: Determine PPE Category

Calculator Results Summary:

Scenario

A 4160V medium-voltage switchgear with high available fault current. This represents a more severe arc flash hazard typical in large industrial facilities or utility substations.

Given:

• System Voltage: 4160V (three-phase, line-to-line)
• Bolted Fault Current: 40 kA (from short circuit study)
• Equipment Type: Switchgear
• Electrode Configuration: VCB (Vertical conductors in box)
• Conductor Gap: 104 mm (typical for 4.16kV)
• Enclosure Height: 660 mm
• Enclosure Width: 660 mm
• Enclosure Depth: 660 mm
• Working Distance: 610 mm (24 inches, typical for MV switchgear)
• Clearing Time at I_arc: 300 ms (from relay coordination study)
• Clearing Time at I_arc-min: 400 ms (longer due to inverse time characteristic)
• Incident Energy Threshold: 1.2 cal/cm²

Step 1: Calculate Arcing Current at Anchor Points

For 4160V, interpolation required between 2700V and 14300V anchor points.

Calculate I_arc at 2700V using VCB coefficients from Table 3:

Calculate I_arc at 14300V using VCB coefficients from Table 5:

Interpolate for 4160V:

Step 2: Calculate Reduced Arcing Current

Step 3: Calculate Correction Factor

Enclosure is "Typical" (V > 600V, dimensions > 508mm).

Larger enclosure increases CF above 1.0, which will reduce calculated incident energy.

Step 4: Calculate Incident Energy at I_arc

Using interpolated IE values between 2700V and 14300V anchor point calculations:

Step 5: Calculate Incident Energy at I_arc-min

Using I_arc-min = 24.6 kA, T = 400 ms (33% longer than nominal case):

Step 6: Determine Final Incident Energy

Again, the reduced arcing current scenario with longer clearing time produces the worst-case incident energy, approximately 27% higher than the nominal case.

Step 7: Calculate Arc Flash Boundary

The arc flash boundary extends well beyond the working distance, indicating significant arc flash hazard.

Step 8: Determine PPE Category

Calculator Results Summary:

Engineering Observations:

• Medium-voltage systems produce significantly higher incident energy than low-voltage systems even with similar fault current levels
• The 300-400 ms clearing time is relatively long for this voltage level; faster protection would substantially reduce incident energy
• The correction factor of 1.123 provides approximately 11% reduction in incident energy compared to an open-air configuration
• The arc flash boundary of 2.3 meters emphasizes the need for proper approach boundaries and qualified worker requirements per NFPA 70E

• IEEE Std 1584-2018, IEEE Guide for Performing Arc-Flash Hazard Calculations
• NFPA 70E-2021, Standard for Electrical Safety in the Workplace
• NEC 2020, Article 110.16, Flash Protection
• IEEE Std 1584a-2004 (superseded by 2018 edition)
• IEEE Std 1584b-2011 (superseded by 2018 edition)

IEEE 1584-2018 provides calculation methodology for incident energy and arc flash boundaries. NFPA 70E provides the electrical safety framework including:

• PPE requirements and categories (Table 130.5(G))
• Approach boundary definitions (limited, restricted, prohibited)
• Voltage-rated glove requirements (Table 130.7(C)(7)(a))
• Energized electrical work permit requirements
• Safety-related work practice requirements

Both standards must be consulted for complete arc flash hazard analysis and electrical safety program development. IEEE 1584 provides "how much energy," while NFPA 70E provides "how to work safely."