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Arc flash: incident energy and arc flash boundary

Conservative estimate of incident energy and arc flash boundary for open-air arcs, using Lee's theoretical method for AC and the maximum power method for DC. It is not an IEEE 1584 study: labels and final clothing come from a formal study.

OSHA 29 CFR 1910.269§ ap. Eaccepted methods and working distancesIEC 60909-0bolted fault current

Example cases
Arc flash: incident energy and arc flash boundary

Only the basic data; the rest is taken with typical values.

ALearn

E1System
V

Phase-to-phase for AC; the source voltage for DC.

Both methods are valid in open air only. For enclosures the tool gives no number.

E2Bolted fault current
kA

Symmetrical three-phase at the bus; take it from the short-circuit tool.

MVA

At the transformer primary; provided by the utility.

kVA

0 = no transformer.

%
E3DC fault current
kA

The battery or converter manufacturer's value.

mΩ

Internal battery resistance plus cables and joints.

E4Clearing time and distance
s

Relay or fuse plus breaker opening; read it from the coordination study.

mm

From the arc to the face and chest. Typical values (OSHA): LV cables and panels 455 mm, LV switchgear 610 mm, 5 and 15 kV switchgear 910 mm.

E5Criterion
cal/cm²

Use a decimal point. The calculation runs in your browser and updates as you type.

Incident energy

— cal/cm²

Arc flash boundary

—

Energy band and minimum arc rating

—

Bolted fault current

— kA

Maximum arc power

— MW

Incident energy vs. clearing time
  • Energy
  • Band limits
  • Your time
At the working distance, incident energy grows linearly with arc duration. The dashed lines mark 1.2, 4, 8, 25 and 40 cal/cm².
Incident energy vs. distance
  • Energy
  • Boundary threshold
  • Working distance
Energy falls with the square of the distance. The arc flash boundary is where the curve crosses the threshold.
Incident energy vs. fault current
  • Energy and its duration
  • Your current
At a fixed clearing time, less current gives less energy. But a smaller fault may be cleared more slowly: check the time the protection gives at minimum fault current.

Step-by-step calculation

What it means for your installation

    Need it for a real project? We carry out the full study, with its report.

    Design and studiesSend via WhatsAppGo to the contact form

    What it is for

    Use it for a first look at arc flash risk at a point in the installation: how much energy would reach the working distance, how far the arc flash boundary extends and how much everything changes with the clearing time. It uses open theoretical methods that give a result on the safe side, so it is good for screening and comparing, not for labelling.

    This is not an IEEE 1584 study or an NFPA 70E analysis. Equipment labels and final clothing require a formal arc flash study, with the system model, the protection coordination and a method validated by testing for each type of equipment.

    The bolted fault current comes from the short-circuit tool, and the clearing time from relay coordination. The three tools use the same data names, so you can move from one to another with the link.

    How it is calculated

    AC, open-air arc: Ralph Lee's theoretical method

    Dc = (2.65 · MVAbf · t)½ [ft] · MVAbf = √3 · V · Ibf · E = 1.2 · (Dc / D)² cal/cm²

    Lee (IEEE Transactions on Industry Applications, 1982) assumed an inductive system and a resistive arc, so the arc draws half of the bolted-fault power, and called Dc the curable-burn distance, where the energy is 1.2 cal/cm². With the inverse-square law of distance, the energy at any distance follows; in kV, kA and mm it equals E ≈ 5.12 × 10⁵ · V · Ibf · t / D² cal/cm². Open sources: the text of Lee's equation quoted in patent US 9146267 B2 (USPTO), appendix E of OSHA 29 CFR 1910.269 and UFC 3-560-01.

    DC, open-air arc: maximum power

    Parc = V · Ibf / 4 · E = Parc · t / (4π · D²)

    By the maximum power transfer theorem, the arc draws the most power when its voltage is half the source voltage (assumption of D. R. Doan, 2007). That power spreads over a sphere of radius D. It is an upper bound: the real arc draws less.

    IEC 60909-0equivalent voltage source

    Bolted fault current and units

    Ibf = c · Un / (√3 · |ZQ + ZT|) · 1 cal/cm² = 4.184 J/cm²

    With "Network and transformer", the current comes from the same IEC 60909 calculation as the short-circuit tool, using cmax. The arc flash boundary is the distance at which the energy drops to the chosen threshold. The energy band is calculated from the result (below 1.2; 1.2 to 4; 4 to 8; 8 to 25; 25 to 40; above 40 cal/cm²) and the minimum arc rating equals the estimated energy: the arc rating of the clothing must be equal to or greater than the estimated incident energy, as OSHA 1910.269 requires.

    Limits of the calculation

    • It is a conservative screening estimate. It is not an IEEE 1584 study, it does not reproduce NFPA 70E tables and it cannot be used to make equipment labels.
    • Open-air arcs only. Inside an enclosure or switchgear cell, Lee's method underestimates the energy, according to OSHA, and the tool gives no number.
    • For AC, the method is reasonable for three-phase open-air arcs up to 600 V, conservative between 600 V and 15 kV and extremely conservative above 15 kV (OSHA). For DC, maximum power is an upper bound.
    • You enter the clearing time. It must come from the actual protection curve at the current flowing during the arc, plus the breaker opening time; at minimum fault current the protection can be considerably slower.
    • It does not consider the motor contribution that decays during the fault, a moving arc or the blast (pressure, shrapnel, sound). The energy band is not a PPE category of any standard.

    Frequently asked questions

    Does this tool replace an arc flash study?

    No. It is a conservative screening estimate: it tells you whether a point deserves attention and how much the clearing time matters. Equipment labels and the final choice of clothing come from a formal study, with the system model, the protection coordination and a method validated by testing for each type of equipment.

    Why is the result so high at medium voltage?

    Lee's method assumes the arc draws the maximum power the network can deliver. At medium and high voltage the arc voltage is a small fraction of the system voltage, so the real power is much lower. OSHA considers it conservative above 600 V and extremely conservative above 15 kV.

    Why does it not calculate arcs inside an enclosure?

    Inside an enclosure the heat leaves concentrated through the opening. OSHA found that Lee's equation underestimates the energy of a three-phase arc in an enclosure, so the tool gives no number that could end up on the unsafe side. Enclosed panels and switchgear need a formal study.

    What is the arc flash boundary?

    It is the distance from the arc at which incident energy falls to 1.2 cal/cm², the threshold of a curable second-degree burn. Inside that radius, anyone exposed needs clothing with an arc rating equal to or greater than the estimated energy.

    We carry out your arc flash study to IEEE 1584 · request a quote

    We model your system, review the protection coordination and calculate incident energy and the arc flash boundary at every panel and switchgear cell, with a report for the labels. We use the IEEE 1584 method and commercial software; this tool uses open methods only, for screening.

    See design and studiesSee the coordination study

    Related guides

    Arc Flash Study: IEEE 1584 and NFPA 70EWhat an arc flash study is, when codes and insurers ask for one, how IEEE 1584-2018 calculates incident energy, and the PPE categories in NFPA 70E.Arc Flash PPE Categories: How They Are DefinedWhat NFPA 70E PPE categories 1 to 4 are, the arc rating each requires, and when to use the tables or an incident energy calculation.Arc Flash Labels: What They Must SayWhat an arc flash label must show under NFPA 70E and the NEC, where the data comes from, how far IEEE 1584 supports it and when to replace the label.Arc flash relay: light-detection arc flash protectionHow light and current arc flash protection works: sensors, zones, which breaker it trips, operating times, IEC 61850 (SARC) and testing.

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