When to use this calculator

UL listed equipment typically carries a single interrupting or short-circuit rating in symmetrical RMS amperes. It is not always sufficient to only compare that rating to the calculated symmetrical fault current.

Ratings are given based on testing at a specific X/R ratio. The X/R ratio drives how much DC offset it carries in the first cycle, and subsequently how high its peak and asymmetrical RMS current rise. When the calculated X/R is higher than the test X/R, the peak or asymmetrical current that the equipment was tested to can be exceeded, even while the symmetrical current is below its rating.

For example, a 65kA breaker (test X/R=4.9) with 60kA (X/R=12) available passes on symmetrical current alone. Its first-cycle peak, however, is 150 kA against 140 kA tested. The breaker is overdutied.

IEEE C37.13 simplifies this process by calculating a multiplication factor that adjusts the calculated RMS symmetrical current to account for this. Therefore, the adjusted current can be directly compared to the published equipment rating.

Low Voltage Duty Calculator

Select whatever inputs are available and enter their values. The calculator automatically determines which additional parameters can be calculated.

Equipment

Rating type

Interrupting Withstand

Compares calculated duty with the interrupting rating.

Equipment type Test X/R and duty basis are selected based on equipment type and standard. Choose Custom to manually select.

Governing duty basis

Peak Asymmetrical RMS Worst case (larger MF)

See duty basis notes.

1. Select Known Parameters

Select each input that's known.

2. Enter Known Values

Enter the known inputs here to calculate the values to the right.

Example: UL 489 molded case breaker rated 35 kA interrupting, with 30 kA available at X/R 7.

Equations and calculation basis

First-cycle asymmetry

I_sym is the calculated ANSI symmetrical RMS fault current. X/R is the calculated X/R ratio of the fault.
Both factors assume maximum DC offset, evaluated one half cycle after fault initiation (IEEE 3002.3 Eq. 66 and 67).

Asymmetrical RMS factor and current: K_asym(X/R) = √(1 + 2e^−2π/(X/R))
I_asym = I_sym × K_asym(X/R)
Peak factor and current: K_peak(X/R) = √2 × (1 + e^−π/(X/R))
I_peak = I_sym × K_peak(X/R)
X/R from asymmetrical RMS current: X/R = −2π / ln[((I_asym / I_sym)² − 1) / 2]
Valid for 1 ≤ I_asym / I_sym < √3
X/R from peak current: X/R = −π / ln[I_peak / (√2 × I_sym) − 1]
Valid for √2 ≤ I_peak / I_sym < 2√2

Equipment capability

I_rated is the symmetrical RMS interrupting or withstand rating, demonstrated at the test X/R.

Tested asymmetrical and peak capability: I_asym,tested = I_rated × K_asym(X/R_test)
I_peak,tested = I_rated × K_peak(X/R_test)
Test power factor and X/R: PF_test = 1 / √(1 + (X/R_test)²)
X/R_test = √(1 − PF_test²) / PF_test

Duty multiplication factors and pass/fail

The max[1, …] term ensures multiplication factor is never below 1. When the system X/R is at or below the test X/R, MF = 1.

Asymmetrical RMS multiplying factor: MF_asym = max[1, K_asym(X/R) / K_asym(X/R_test)]
= max[1, √((1 + 2e^−2π/(X/R)) / (1 + 2e^{−2π/(X/R_test)}))]
Peak multiplying factor (C37.13 / SKM LVF): MF_peak = max[1, K_peak(X/R) / K_peak(X/R_test)]
= max[1, (1 + e^−π/(X/R)) / (1 + e^{−π/(X/R_test)})]
Adjusted symmetrical duty: I_adj = I_sym × MF
MF = MF_peak or MF_asym, per the governing duty basis
Worst case: MF = max(MF_peak, MF_asym)
Pass/fail: ANSI comparison: pass when I_rated ≥ I_adj
Direct comparisons, which give the same result:
I_rated ≥ I_sym, and
Peak basis: I_peak,tested ≥ I_peak
Asymmetrical RMS basis: I_asym,tested ≥ I_asym
Worst case: both of the above

Pass/fail should use the duty basis applicable to the equipment rating and test standard. Peak current relates to mechanical stress, asymmetrical RMS current relates to heating. SKM uses peak, ETAP defaults to asymmetrical RMS, while worst case is the most conservative.

Standard test X/R ratios

This table shows typical short-circuit test power factors from UL and ANSI equipment standards. The test X/R corresponds to the highest power factor permitted in each range. K_asym and K_peak are the tested asymmetrical RMS and peak capabilities per unit of the symmetrical rating. Duty basis is the RMS symmetrical multiplication factor that gets applied to determine Pass/Fail.

Equipment	Standard	Short-circuit rating	Test PF	Test X/R	K_asym	K_peak	Duty basis
LV power circuit breaker, unfused	ANSI C37.13 / UL 1066	All	15%	6.6	1.331	2.293	Peak1
LV metal-enclosed switchgear	ANSI C37.20.1 / UL 1558	All	15%	6.6	1.331	2.293	Peak1
LV power circuit breaker, fused	ANSI C37.13 / UL 1066	All	20%	4.9	1.247	2.159	Asym RMS2
Low-voltage fuse	UL 248	All	≤ 20%	4.9	1.247	2.159	Asym RMS3
Molded and insulated case circuit breakers	UL 489	≤ 10 kA	45–50%	1.7	1.025	1.637	Peak4
		10–20 kA	25–30%	3.2	1.132	1.944
		> 20 kA	15–20%	4.9	1.247	2.159
Panelboards, switchboards and motor control centers	UL 67 / UL 891 / UL 845	≤ 10 kA	45–50%	1.7	1.025	1.637	Peak4
		10–20 kA	25–30%	3.2	1.132	1.944
		> 20 kA	15–20%	4.9	1.247	2.159
Transfer switches	UL 1008	≤ 10 kA	40–50%	1.7	1.025	1.637	Peak4
		10–20 kA	25–30%	3.2	1.132	1.944
		> 20 kA	≤ 20%	4.9	1.247	2.159

Use manufacturer's published test data if available.

Duty basis notes

Peak basis. IEEE C37.13 (Table 3 multiplying factors) and IEEE 3002.3-2018 Eq. 67 rate unfused low-voltage power circuit breakers on first-cycle peak current. SKM software uses this methodology for equipment evaluation as can ETAP as an option.
Asymmetrical RMS basis. IEEE 3002.3-2018 Eq. 66 gives the first-cycle asymmetrical RMS current and associates it with fused low-voltage power circuit breakers.
Asymmetrical RMS basis, by extension of IEEE 3002.3 Eq. 66 to standalone fuses, which respond to asymmetrical RMS (heating) current. Not stated explicitly for UL 248 fuses. Confirm with the fuse manufacturer.
Peak basis, common industry practice (e.g. using SKM or ETAP software) for UL 489 molded and insulated case breakers. Transfer switches and other assemblies are assumed to to use peak basis as well.

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