How to Calculate an Arc Flash Boundary

Review the calculation objective

Confirm that your objective is to calculate the incident energy for an arc flash event, continuing from a previously calculated arcing current. This calculation follows NFPA 70E, Annex D.4.3, section D.3, for incident energy.

Review the basic incident energy formula

Refer to the basic formula for normalized incident energy at working distance:

lg En = k1 + k2 + [1.081 × (lg Ia)] + 0.0011G

• lg denotes log base 10.
• En is the normalized incident energy (J/cm²).
• Ia is the arcing current (previously calculated).
• G is the conductor gap in millimeters.
• k1 and k2 are constants based on arc type and system grounding.

Identify your system parameters and reference Table D.4.2

For this example, the system is a 480VAC Panel with a bolted three-phase short circuit current of 30,000A. Use the following constants and variables:

• k1 = -0.792 for open air arcs, or -0.555 for arcs-in-a-box (use -0.555 for a panel board).
• k2 = 0 for ungrounded/high-resistance systems, or -0.113 for grounded systems (use -0.113 for this grounded system).
• G = 25 mm, the typical conductor gap for panel boards.
• Ia = 16 kA, the previously calculated arcing current.

Reference Table D.4.2 for the conductor gap and distance exponent: for MCCs and panels, the typical conductor gap is 25 mm and the distance exponent is 1.641.

Substitute values into the formula

Substitute the constants and calculated values into the formula:

lg En = -0.555 + (-0.113) + [1.081 × (lg 16.761)] + 0.0011 × 25

Calculate each term step by step:

• lg 16.761 ≈ 1.224
• 1.081 × 1.224 ≈ 1.323
• 0.0011 × 25 = 0.0275
• Sum: -0.555 + (-0.113) + 1.323 + 0.0275 ≈ 0.68298

The result is lg En = 0.68298.

Calculate the normalized incident energy

Remove the logarithm by raising 10 to the calculated power:

En = 10^(0.68298) ≈ 4.81925 J/cm²

This is the normalized incident energy at the working distance for the given system parameters.

Apply the full incident energy formula

The value calculated in the previous step is the normalized incident energy, not the actual incident energy at the working distance. To find the actual incident energy (E), use the full formula:

E = 4.184 × Cf × En × [(t / 0.2) × (610^x / D^x)]

• E = incident energy (J/cm²)
• Cf = constant factor (1.0 if V > 1kV, 1.5 if V ≤ 1kV)
• En = normalized incident energy (J/cm²)
• t = arcing time (seconds)
• x = distance exponent (from Table D.4.2)
• D = working distance (mm)

Example substitution:

E = 4.184 × 1.5 × 4.81925 × [(0.0167 / 0.2) × (610 / 455)^1.641]

Select the correct constant factor (Cf)

Choose the constant factor based on system voltage:

• For systems with voltage ≤ 1kV, use Cf = 1.5.
• For systems with voltage > 1kV, use Cf = 1.0.

In this example, the system voltage is 480V, so set Cf = 1.5.

Determine the arcing time (t)

The arcing time (t) is determined by the time-current characteristic of your overcurrent protection device (fuse or circuit breaker).

Safety note: Do not use the bolted three-phase fault current for this calculation. Always use the arcing current (previously calculated as 16.7 kA) to find the trip time from the manufacturer's time-current curve, since the bolted fault current does not represent arc flash conditions. In this example, the trip time for 16.7 kA is 0.0167 seconds, so use t = 0.0167.

Reference the distance exponent and working distance

Use Table D.4.2 to find the distance exponent (x) for your equipment type and voltage class. For a 480V panel (MCCs and panels, 0.208–1 kV):

• Typical conductor gap: 25 mm
• Distance exponent: 1.641

Use the working distance (D) specified for your system (in this example, 455 mm).

Substitute all values and calculate the incident energy

Substitute all determined values into the formula:

• Cf = 1.5
• En = 4.81925
• t = 0.0167 seconds
• x = 1.641
• D = 455 mm

The formula becomes:

E = 4.184 × 1.5 × 4.81925 × [(0.0167 / 0.2) × (610 / 455)^1.641]

Performing this calculation gives a result of E = 4.086 J/cm².

Convert incident energy to calories per square centimeter

Convert the result from joules to calories using the conversion factor 1 cal = 4.184 J:

E = 4.086 J/cm² ÷ 4.184 = 0.977 cal/cm²

This cal/cm² value is what you use to determine the hazard risk category for PPE selection and to support the arc flash boundary determination for the equipment label.

Confirm unit conversion and methodology flexibility

Always convert your final incident energy value to cal/cm², since this is the standard unit referenced in arc flash labeling and PPE requirements.

Note that the NFPA 70E Annex D.4.3 formulas and the previously calculated arcing current allow you to mix and match variables to fit your system:

• Adapt the constants for grounded or ungrounded systems.
• Apply the method to different equipment types, such as switchgear or panel boards.
• Adjust the conductor gap, distance exponent, and working distance for your specific equipment.

This approach is customizable across system configurations, which makes it a reliable choice for calculating incident energy. Other calculation methods are also available in NFPA 70E Annex D.4, and you may select whichever method best fits your system and needs.