Voltage Regulation Calculator (no-load vs full-load, transformer %R and %X)

Understanding the voltage regulation calculator — concept and principle

Voltage regulation tells you how much a power source's output voltage falls when it goes from no load to full load. This calculator finds it either from two measured voltages or, for a transformer, from its percentage resistance and reactance and the load power factor. It is used for transformers, generators and power supplies.

A 10 V sag under load is 4.35 % regulation.

How it is calculated

Measured method: VR = (VNL − VFL) ÷ VFL × 100 %

Transformer method: VR ≈ εr cos φ ± εx sin φ + (εx cos φ ∓ εr sin φ)² ÷ 200

Full-load voltage = VNL ÷ (1 + VR ÷ 100)

VNL no-load voltage, VFL full-load voltage.
εr and εx are the resistance and reactance drops in % of rated voltage (from the short-circuit test); cos φ is the load power factor. Upper signs apply to lagging (inductive) loads, lower signs to leading (capacitive) loads.

The principle

Every real source has internal impedance. When current flows, part of the source voltage is used up inside, so less reaches the terminals. Regulation expresses that loss relative to the full-load voltage. In a transformer, resistance causes a drop in phase with the current, and leakage reactance causes a drop 90° ahead of it. How these add to the output depends on the load's phase angle: with lagging loads the reactive drop adds strongly, while a leading load can make the output voltage rise, giving negative regulation. The squared term is a small correction for the angle between the voltages.

Worked example

Default inputs: measured method, VNL = 240 V, VFL = 230 V.

Voltage drop = 240 − 230 = 10 V.
VR = 10 ÷ 230 × 100 = 4.35 %.
Full-load voltage = 230 V, which is 230 ÷ 240 × 100 = 95.83 % of no-load.
The power-factor angle applies only to the transformer method, so it shows —.

Each point is the calculator re-run with only “Full-load voltage (V, measured method)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Full-load voltage (V, measured method)	Voltage regulation (%)
57.5	317.39
115	108.7
172	39.13
230	4.35
288	-16.52
345	-30.43
460	-47.83

How to read the result

Lower regulation means a stiffer source whose voltage holds up under load. Large power transformers typically have low regulation at unity power factor, rising at low lagging power factors. A regulated electronic power supply should be close to 0 %. If regulation is too high for sensitive equipment, consider a larger transformer, tap changing or power-factor correction.

Common mistakes

Dividing by the no-load voltage instead of the full-load voltage.
Measuring the two voltages at different input voltages or temperatures.
Using the wrong sign convention for leading loads.
Confusing percentage impedance with regulation; they are related but not equal.

Keep in mind: The transformer formula is an approximation using rated values. For equipment selection or protection settings use the manufacturer's test data and a qualified engineer.

Frequently asked questions

Can voltage regulation be negative?

Yes, with a leading (capacitive) load the output voltage can rise above the no-load value.

Why divide by the full-load voltage?

That is the conventional definition; some texts use the no-load voltage, which gives a slightly smaller number.

Where do εr and εx come from?

From the transformer's short-circuit test or nameplate impedance and load-loss data.

Sources: Standard power-engineering formulas: voltage regulation referred to full-load voltage and the transformer approximation from per-unit resistance and reactance

Checked 9 Nov 2026. Definition of voltage regulation (no-load minus full-load, referred to full-load) and the transformer approximation from per-unit resistance and reactance — standard formulas (IEC/IEEE transformer practice).

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