Enter incident energy at a known working distance and a new distance to estimate incident energy at the new distance using a simple inverse-square relationship. This does not calculate arc-blast/overpressure.

Arc Flash Incident Energy at Distance Calculator

Enter incident energy at a reference distance and a new distance to estimate incident energy at the new distance (inverse-square approximation).

Arc Flash Incident Energy vs Distance Formula (Inverse-Square Approximation)

The following formula is a simplified inverse-square relationship that is sometimes used as a rough estimate for how incident energy changes with distance in open air. It is not an arc-blast/overpressure (pressure) formula, and real arc-flash incident-energy calculations (e.g., IEEE 1584) are more complex.

E_2 = E_1\left(\frac{d_1}{d_2}\right)^2

Variables:

  • E1 is the incident energy at the reference distance (commonly in cal/cm²)
  • d1 is the reference distance (use the same distance units as d2)
  • d2 is the new distance (use the same distance units as d1)
  • E2 is the estimated incident energy at the new distance (commonly in cal/cm²)

To estimate incident energy at a new distance using this approximation, multiply the reference incident energy by the square of the ratio of reference distance to new distance.

What is an Arc Flash?

An arc flash is a type of electrical explosion or discharge that results from a low-impedance connection through the air to ground or another voltage phase in an electrical system. When an arc flash occurs, it can cause significant damage, including severe burns, hearing loss, and even death. The intense heat and pressure generated by an arc flash can vaporize metal and create a blast wave that can knock workers off their feet.

How to Estimate Arc Flash Incident Energy at a Different Distance?

The following steps outline how to estimate incident energy at a different distance using the inverse-square approximation.

  1. First, determine the incident energy at a known reference distance (E1).
  2. Next, determine the reference distance (d1) and the new distance (d2).
  3. Finally, calculate the estimated incident energy at the new distance using E2 = E1 × (d1/d2)².
  4. After inserting the values and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge (inverse-square approximation).

Incident Energy (E1) = 8 cal/cm²

Reference Distance (d1) = 20 cm, New Distance (d2) = 40 cm, Estimated Incident Energy (E2) = 8 × (20/40)² = 2 cal/cm²