Estimate arc flash incident energy at a new distance from reference energy and distance using inverse-square scaling and unit conversion.
Arc Flash Incident Energy at Distance Formula
The calculator estimates incident energy at a new working distance using an inverse-square approximation. It assumes the reference incident energy is known at one distance, then scales that energy based on the ratio of the two distances.
E_2 = E_1 * (d_1 / d_2)^2
- E1 = incident energy at the reference distance
- E2 = estimated incident energy at the new distance
- d1 = reference distance
- d2 = new distance
The calculator first converts the entered incident energy to cal/cm² and the entered distances to cm. It then applies the inverse-square formula and converts the result to your selected output energy unit.
The unit conversions used are:
1 cal/cm^2 = 41840 J/m^2 = 10 kcal/m^2 = 41.84 kJ/m^2
1 m = 100 cm, 1 in = 2.54 cm, 1 ft = 30.48 cm
This is a distance-scaling estimate only. It is not a full IEEE 1584 arc-flash study and does not account for enclosure effects, electrode configuration, arcing current, clearing time, system voltage, or equipment geometry.
Incident Energy Unit Conversions
| Unit | Equivalent to 1 cal/cm² | Use in calculator |
|---|---|---|
| cal/cm² | 1 cal/cm² | Common arc-flash incident energy unit |
| J/m² | 41,840 J/m² | SI energy per area |
| kcal/m² | 10 kcal/m² | Metric heat energy per area |
| kJ/m² | 41.84 kJ/m² | SI energy per area in larger units |
Distance Change Effect on Incident Energy
| New distance compared with reference distance | Energy multiplier | Meaning |
|---|---|---|
| Half the distance | 4 × | Estimated incident energy is four times higher |
| Same distance | 1 × | Incident energy is unchanged |
| Twice the distance | 0.25 × | Estimated incident energy is one quarter as much |
| Three times the distance | 0.111 × | Estimated incident energy is about one ninth as much |
Example Problems
Example 1: Estimate energy farther away
You have an incident energy of 8 cal/cm² at a reference distance of 18 in. Estimate the incident energy at 36 in.
E_2 = 8 * (18 / 36)^2
E_2 = 8 * 0.25 = 2 cal/cm^2
The estimated incident energy at 36 in is 2 cal/cm².
Example 2: Estimate energy closer to the source
You have an incident energy of 5 cal/cm² at 100 cm. Estimate the incident energy at 50 cm.
E_2 = 5 * (100 / 50)^2
E_2 = 5 * 4 = 20 cal/cm^2
The estimated incident energy at 50 cm is 20 cal/cm².
FAQ
Is inverse-square scaling valid for all arc-flash calculations?
No. The inverse-square method is only a rough distance-scaling approximation. Real arc-flash behavior is affected by enclosure size, conductor spacing, electrode orientation, arcing current, arc duration, voltage, and other equipment-specific factors. Use a proper arc-flash study for safety labeling, PPE selection, and compliance decisions.
Why does incident energy increase so quickly when distance decreases?
The formula squares the distance ratio. If you cut the distance in half, the ratio becomes 2, and 2 squared is 4. That means the estimated incident energy becomes four times higher. Small changes in working distance can have a large effect on the result.
What unit should you use for arc-flash incident energy?
Arc-flash incident energy is commonly expressed in cal/cm², especially for PPE and arc-rated clothing comparisons. The calculator also supports J/m², kcal/m², and kJ/m² when your source data uses metric energy-per-area units.