The voltage regulation calculator above measures one property of a power source: how much its output voltage changes between having nothing connected and delivering its rated load. A perfect source would not change at all. A real transformer, generator, feeder or power supply has internal impedance, that impedance carries the load current, and the voltage lost inside the source never reaches the terminals. Percent regulation is the standard way of quoting that behaviour on a nameplate.
This is a different question from the one the voltage drop calculator answers, and Arb Digital publishes both because the two are routinely confused. That page computes the volts lost along a run of cable from its length, gauge and current, and it treats the supply as fixed. This page treats the source itself as the thing with impedance and expresses the result as a percentage figure of merit that can be compared between machines. The cable answer is in volts and depends on how far away the load is. The regulation answer is dimensionless and belongs to the equipment.
What This Voltage Regulation Calculator Does
Two routes lead to the same number. If you have a bench, the direct route is to measure the terminal voltage with the load disconnected, connect the rated load, and measure again. The difference divided by the loaded voltage is the regulation. That method needs no knowledge of what is inside the source.
If you are working from a datasheet or a short-circuit test instead, the second route uses the equivalent circuit: a resistance and a reactance in series with an ideal source, both referred to the same side of the transformer. The load current flowing through them produces a drop whose size depends not only on the current but on the phase angle between current and voltage. That phase dependence is the part people underestimate, and it is why the same transformer quotes different regulation figures at different power factors.
The tool computes the regulation on the full-load base, which is the conventional definition, and also reports the alternative no-load base that some references use. It shows the no-load voltage, the change in volts, and how the resistive and reactive parts of the impedance each contribute.
How to Use It
- Choose your method. Two measured voltages if you tested it, or impedance and power factor if you are predicting from data.
- Keep everything on one side. Voltage, current, resistance and reactance in the impedance method must all be referred to the same winding. Mixing primary and secondary values is the single most common error.
- Enter the power factor of the load, not of the source. A motor load is inductive and lagging; a long lightly loaded cable or a capacitor bank can be leading.
- Read both bases. The headline uses the full-load voltage as the denominator, which is the usual convention, but some datasheets divide by the no-load voltage instead and quote a slightly smaller number.
- Watch for a negative result. With a leading load the terminal voltage can rise under load. That is a real effect, not an error.
The Formula and a Worked Example
From two measurements the definition is simply
Regulation % = (Vno load − Vfull load) ÷ Vfull load × 100
From the equivalent circuit, the no-load voltage is the phasor sum of the terminal voltage and the internal drop. Taking the terminal voltage as reference and resolving the current into components in phase and in quadrature with it:
E = √[(V cosθ + I Req)² + (V sinθ ± I Xeq)²]
with the plus sign for a lagging load and the minus sign for a leading one. The widely quoted approximation Regulation % ≈ I (Req cosθ ± Xeq sinθ) ÷ V × 100 drops a second-order term. It is accurate to a few hundredths of a percentage point on a strongly lagging load, and drifts to around a tenth of a point at unity power factor where the neglected quadrature term matters more. This tool computes the exact phasor magnitude and reports the approximate figure alongside it.
Work the default through by hand. A transformer delivering 230 V at 20 A into a load of 0.8 power factor lagging, with Req = 0.2 Ω and Xeq = 0.5 Ω, has cosθ = 0.8 and sinθ = 0.6. The in-phase component is 230 × 0.8 + 20 × 0.2 = 184 + 4 = 188 V, and the quadrature component is 230 × 0.6 + 20 × 0.5 = 138 + 10 = 148 V. The no-load voltage is √(188² + 148²) = √57248 = 239.27 V, so the regulation is (239.27 − 230) ÷ 230 = 4.03 per cent. The approximation gives 20(0.2 × 0.8 + 0.5 × 0.6) ÷ 230 = 9.2 ÷ 230 = 4.00 per cent, which is the same answer to within three hundredths. Transformer equivalent circuits and the tests that populate them are covered in MIT OpenCourseWare's Introduction to Electric Power Systems.
Why Power Factor Changes the Answer So Much
Run the same transformer at unity power factor and the regulation falls from 4.03 per cent to about 1.83 per cent. Run it at 0.8 leading and it goes negative, roughly −1.11 per cent: the terminal voltage is higher with the load connected than without it. Nothing about the transformer changed. Only the phase of the current did.
The reason is geometric. The internal drop is a phasor, and what matters is not its length but how much of it lies along the terminal voltage. On a lagging load the reactive drop points broadly the same way as the terminal voltage and adds almost its full length. On a leading load it points partly against the terminal voltage and subtracts. At unity power factor the reactive drop is almost entirely at right angles to the terminal voltage and changes its magnitude only weakly, which is why a reactance that dominates the impedance can still contribute less to the regulation than a much smaller resistance.
Two practical consequences follow. First, a regulation figure without a power factor attached is close to meaningless, and a nameplate that quotes one is quoting it at an assumed condition you should look up. Second, correcting the power factor of a load changes the voltage the load sees, which is one of the reasons capacitor banks are installed on distribution feeders at all. The power factor calculator handles the correction arithmetic, and the RMS voltage calculator covers the waveform side of what a meter is actually reading.
The Same Idea Under Different Names
Voltage regulation is one member of a family of source-stiffness measures that share a definition and differ in vocabulary.
A battery is normally described by its internal resistance rather than by a regulation percentage, but the physics is identical: terminal voltage falls as the product of internal resistance and current. The internal resistance calculator derives that resistance from a loaded and unloaded measurement, which is the same pair of readings the measured method here uses.
A bench power supply distinguishes load regulation, the change when the current changes, from line regulation, the change when the mains input changes. Both are quoted as percentages and both are usually far tighter than a transformer's, because a regulated supply corrects the error with feedback rather than tolerating it.
A distribution feeder is usually described by the voltage at the far end as a percentage of nominal, because a utility cares about what the customer receives rather than about the transformer alone. That figure combines the transformer's regulation with the cable drop, so both this page and the voltage drop calculator feed into it, along with the conductor sizing from the wire size calculator.
What Gets This Wrong in Practice
The impedance method is only as good as the side you referred the values to. Impedances referred through a transformer scale with the square of the turns ratio, so a resistance of 0.2 Ω on the secondary appears as a very different number on the primary. If your short-circuit test was done from the high-voltage side, the resulting impedance is a high-voltage-side quantity and must be used with high-voltage-side current and voltage, or transferred first. The transformer turns ratio calculator gives the ratio that transfer needs.
Temperature matters too. Winding resistance rises by roughly four tenths of a per cent per kelvin for copper, so a transformer that is warm from hours of full load has a measurably larger resistive component than the same unit cold on a test bench. Standard practice is to correct measured resistance to a stated reference temperature before quoting regulation, and to say which temperature was used. Reactance is far less temperature-sensitive, so on a lagging load the effect is smaller than it first appears — but at unity power factor, where the resistive term dominates, it is the whole story. The basic circuit relations behind all of this are laid out in MIT's 6.002 Circuits and Electronics and, more informally, in Georgia State University's HyperPhysics reference.
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Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Mixing primary and secondary quantities — impedances transfer with the square of the turns ratio, so every value in the impedance method must be referred to the same winding.
- Quoting regulation without a power factor — the same machine reads about 1.8 per cent at unity, 4 per cent at 0.8 lagging and negative at 0.8 leading. The condition is part of the number.
- Dividing by the wrong voltage — the conventional base is the full-load voltage. Dividing by the no-load voltage gives a smaller figure, and comparing the two conventions makes one machine look better than it is.
- Treating a negative result as an error — a leading load genuinely raises the terminal voltage, and lightly loaded cable capacitance does exactly that on long feeders.
- Ignoring winding temperature — copper resistance rises with temperature, so a hot machine regulates worse than the same machine cold, most visibly at high power factor.
Related Free Tools From Arb Digital
For the volts lost in the cable rather than in the source, use the voltage drop calculator, with the wire size calculator for the conductor choice behind it and the wire resistance calculator for the resistance of a specific run. The transformer turns ratio calculator handles referring quantities between windings, the power factor calculator covers the phase angle that drives everything on this page, and the internal resistance calculator applies the same loaded-versus-unloaded measurement to a battery. For the underlying circuit arithmetic, the Ohm's law calculator is the starting point. Everything Arb Digital publishes is listed on the free online tools hub.
Frequently Asked Questions
Voltage drop is the volts lost along a conductor, computed from its length, cross-section and current, and it treats the supply as fixed. Voltage regulation describes the supply itself: how much its terminal voltage falls between no load and full load, expressed as a percentage of the loaded voltage. One is a property of the wiring between source and load, the other is a property of the source, and a full assessment of what a customer receives needs both.
Yes, and it is not an error. With a leading power factor, part of the internal reactive drop opposes the terminal voltage instead of adding to it, so the loaded voltage can exceed the open-circuit voltage. Long lightly loaded cables and capacitor banks produce exactly this condition, and it is why utilities have to manage voltage rise as well as voltage sag.
Conventionally the full-load voltage, giving regulation as the change divided by the loaded value. Some references divide by the no-load voltage instead, which yields a slightly smaller percentage from the same measurements. This tool reports both so that a figure taken from a datasheet can be compared on the base it was actually quoted on.
Because the internal drop is a phasor and only its component along the terminal voltage changes the magnitude. On a lagging load the reactive drop lies broadly along the terminal voltage and adds nearly all of its length. At unity power factor it lies almost at right angles and contributes far less. On a leading load it partly subtracts. The same impedance therefore produces very different regulation at different load angles.
It depends entirely on the equipment class, so there is no universal figure. Large power transformers are stiff and regulate tightly, small transformers with proportionally larger winding impedance are much looser, and an electronically regulated bench supply corrects the error with feedback and can be tighter again by orders of magnitude. Compare against the manufacturer's stated figure for that class rather than against a rule of thumb.
Yes, through the resistive component. Copper winding resistance rises by roughly four tenths of a per cent per kelvin, so a machine hot from a long run at full load has a larger resistive drop than the same unit cold. Reactance barely changes. The effect is therefore most visible at high power factor, where the resistive term dominates, and standard practice is to correct measured resistance to a stated reference temperature.
Yes, and forgetting is the most common mistake with the impedance method. Resistances and reactances transfer between windings with the square of the turns ratio, while voltages transfer with the ratio itself and currents with its inverse. A short-circuit test performed from the high-voltage side yields a high-voltage-side impedance, and it must be used with high-voltage-side current and voltage or transferred before use.
Figures here come from a standard equivalent-circuit model and are for study and estimation. Electrical installation and equipment ratings are governed by the applicable wiring rules and by the manufacturer's data, and live work should be carried out only by a qualified electrician.
