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Arc-Flash Incident Energy

Also known as incident energy · arc flash energy · cal/cm2 at working distance · Lee point source arc flash · arc flash calculation

E=Parc t4π(4.184×104)D2E = \frac{P_{arc} \, t}{4\pi \left(4.184 \times 10^{4}\right) D^{2}}

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Constant used — built into this formula, no need to enter
cal=4.184 J\mathrm{cal} = 4.184\ \text{J}Calorie (thermochemical) · exact
See also
Arc-Flash Boundary — The same inverse-square curve read the other way: the distance at which this energy has fallen to the burn threshold.Available Short-Circuit Current from Percent Impedance — Where the available fault current that feeds an arcing fault comes from.Transformer Full-Load Current — The nameplate current the percent-impedance short-circuit estimate is built on.

Learning zone

Start with the hard part. This equation sizes a hazard; it does not make work safe. A real arc-flash study begins with the available fault current at the point of work, obtains the arcing current from that, and then reads the protective device's actual clearing time at that arcing current off its time-current curve — and then accounts for whether the arc is in open air or inside an enclosure that reflects energy back at the worker. None of that is knowable from a web page. Do not select PPE, set a label, or authorize energized work from a number produced here. Use this to understand the shape of the problem and to sanity-check a study you have been handed.

The physics is Ralph Lee's, from his 1982 paper on arc-blast burns: treat the arc as a point source, let its energy spread over the surface of a sphere, and the energy landing on any patch falls with the square of the distance. Incident energy is therefore the arc's power multiplied by how long it burns, divided by the area of the sphere at your working distance — and then converted into the calories per square centimetre that every arc-flash document in North America speaks in. That is where the 4.184 × 10⁴ comes from: 4.184 joules per calorie times 10⁴ square centimetres per square metre. IEEE 1584's empirical equations refine the arc power and the fall-off exponent from testing, but the inverse-square skeleton underneath is this one.

Three things fall straight out of it, and they are the reason the equation is worth knowing. Energy is linear in clearing time, so halving the trip time halves the burn — which is why arc-energy-reduction settings, maintenance switches and current-limiting devices do more for a worker than any amount of extra fabric. Energy falls with the square of distance, so an extra 300 mm of reach is worth far more than it feels like. And the Lee point-source model is deliberately conservative in open air; used inside an enclosure, where the arc is focused rather than radiated in every direction, it can read low, which is precisely why the enclosure case needs the tested IEEE 1584 method and not this one.

Arc-Flash Incident Energy
E=Parc t4π(4.184×104)D2E = \frac{P_{arc} \, t}{4\pi \left(4.184 \times 10^{4}\right) D^{2}}
DParctE
Where
  • EE= Incident energy (cal/cm²)
  • ParcP_{arc}= Arc power (W)
  • tt= Arc duration (s)
  • DD= Working distance (m)
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