Methodology
Every number on this site comes from two electrical identities and nothing else. This page states them, derives the three-phase form, proves why power factor never appears, and records the rounding and assumption rules the calculators and charts follow.
The identities
Apparent power S, in volt-amps, is the product of RMS voltage and RMS current. Single-phase, that is the whole story:
Single-phase
S = V × I → I = S ÷ V → amps = kVA × 1000 ÷ volts
The 1000 is only the kilo in kVA: it converts kilovolt-amps back to volt-amps so the units cancel cleanly.
Three-phase
Total apparent power is the sum of the three identical phase contributions: S = 3 × V(L-N) × I. Nameplates quote the line-to-line voltage, and V(L-L) = √3 × V(L-N), so the working form is S = √3 × V(L-L) × I, and its partner S = 3 × V(L-N) × I when the line-to-neutral voltage is the known one. The site's three-phase calculator offers both, and they agree on any correctly paired voltages.
Deriving the three-phase form
The three phase voltages are sinusoids of equal size, displaced by 120°. A line-to-line voltage is the difference of two of them, and phasor arithmetic gives that difference exactly: |Va − Vb| = 2 × V × sin(120° ÷ 2) = 2 × V × (√3 ÷ 2) = √3 × V — a standard result any electrical engineering text derives in its opening chapters.
So: S = 3 × V(L-N) × I = 3 × (V(L-L) ÷ √3) × I = √3 × V(L-L) × I. The √3 is not an empirical constant or a safety factor; it is exact geometry, and it is why 230/400 V, 120/208 V and 277/480 V pair up the way they do (230 × 1.732 ≈ 400, 120 × 1.732 ≈ 208, 277 × 1.732 ≈ 480).
The power-factor proof: why PF never appears
Some widely used calculators ask for a power factor when converting kVA to amps, and apply a default of 0.8 in the denominator. That is an error, and it is provable rather than a matter of opinion. Power factor connects apparent power to real power: kW = kVA × PF. Current connects to real power as: amps = kW × 1000 ÷ (V × PF), single-phase. Substitute the first into the second and the power factor cancels exactly:
The cancellation
amps = (kVA × PF) × 1000 ÷ (V × PF) = kVA × 1000 ÷ V
A tool that keeps the PF only in the denominator computes (kVA × 1000) ÷ (V × PF) — at PF 0.8, a result 25% higher than the true current. It has silently answered a different question (kW to amps, with the kW figure mislabelled as kVA).
The numerical check: 1 kVA at 240 V single-phase is 4.17 A by direct measurement of the identity (1000 ÷ 240). The PF-contaminated formula returns 5.21 A — the current that 1 kW at power factor 0.8 would draw, not the current 1 kVA draws. PF matters enormously for kW, for energy and for generator engine sizing; for the kVA–amps identity it is provably absent. The homepage's power factor section explains this in plain language.
Rounding rules
All displayed results are rounded to two decimal places, with thousands separators, using round-half-up at the boundary. √3 is carried at full double precision through every calculation and never pre-rounded to 1.73 — pre-rounding √3 shifts a 3,000 kVA result by several amps. Chart cells are produced by the same code path as the calculators, so a chart value and a calculator value for the same inputs are always identical.
Worked checks
The build is verified against fixed reference cases, among them: 100 kVA at 400 V three-phase = 144.34 A; 1 kVA at 240 V single-phase = 4.17 A; 500 kVA at 400 V three-phase = 721.69 A; and the reverse identity, 144.34 A at 400 V three-phase = 100.00 kVA. Any change to the calculation code must reproduce these before it ships.
Assumptions
Balanced three-phase loads
Three-phase results assume the load is balanced — equal current on all three phases — which is how nameplate kVA is defined. A badly unbalanced load has one phase above the computed figure; the calculators report the balanced value and say so under the console.
Steady state, nameplate quantities
The identities are steady-state relationships between rated quantities. They do not model motor starting current, inrush, harmonics, voltage drop along a cable run, temperature derating or altitude derating. Those are separate engineering checks, flagged on the pages where they bite (generator starting, transformer inrush). Nothing on this site replaces the electrical code that applies where the work is done, and final designs belong with a licensed electrician or engineer.
No losses in transformer figures
Transformer primary and secondary FLA are both computed from the nameplate kVA, treating the unit as lossless. Real transformers lose a few percent; the nameplate convention — and protection practice — is built on the same lossless statement, so the figures match how the equipment is actually specified.
Sources
The identities are elementary electrical engineering; the voltage systems, protection context and equipment conventions around them rest on these publications. Individual tool pages cite the subset that applies to them.
Standards and references
- NFPA 70 — National Electrical Code — full-load current tables (430.250, 450.3) and the protection framework the worked examples reference.
- IEEE Std 141 — Recommended Practice for Electric Power Distribution — the standard treatment of three-phase power, phasors and per-unit quantities behind the derivations above.
- IEC 60038 — IEC Standard Voltages — the 230/400 V standard voltage system used across most of the world.
- NIST — The Ampere, SI Unit of Electric Current — the definition of the ampere underlying every unit conversion on the site.
- IEEE C57.12.00 — Standard for Liquid-Immersed Distribution and Power Transformers — nameplate ratings and terminology for the transformer tool.