The transformer turns ratio calculator above applies the ideal transformer relations to a two-winding transformer. Give it the number of turns on each winding and the primary voltage and it returns the secondary voltage. Give it the two voltages and the primary turn count and it returns the secondary turns you would have to wind. In both directions it also reports the currents on each side and the impedance the primary circuit appears to see, because those are the numbers that decide whether the rest of the circuit works.
Arb Digital builds free tools that are explicit about the model they use. This page uses the ideal transformer: perfect magnetic coupling, no winding resistance, no core loss, no leakage flux and no magnetising current. That model is exact enough for teaching, for sanity-checking a nameplate and for early design arithmetic, and it is wrong in predictable directions for a real device. Every one of those directions is described below rather than hidden. This is an educational estimate. Mains and high-voltage transformer work must be specified and carried out by a qualified electrician or electrical engineer under the rules that apply in your jurisdiction.
What This Transformer Turns Ratio Calculator Does
A transformer works because a changing current in the primary winding produces a changing magnetic flux in the core, and that same flux threads the secondary winding and induces a voltage in it. If both windings link the identical flux, the voltage induced per turn is the same in both, so the total voltage across each winding is simply proportional to its turn count. OpenStax University Physics Volume 2, section 15.6 on transformers, states the result as Vs/Vp = Ns/Np, and derives the companion current relation Is/Ip = Np/Ns from conservation of power.
Those two relations are the whole of the calculation. The turns ratio, written here as a = Np/Ns, divides the voltage and multiplies the current. A ratio above one is a step-down transformer; below one it steps up. The apparent power is Vs multiplied by Is, identical on both sides in the ideal model, and the impedance seen at the primary is the load impedance multiplied by the square of the ratio.
The load can be entered three ways because people arrive with three different pieces of information: a resistance from a textbook circuit or a resistive heater, a current from a datasheet or a clamp meter, or an apparent power in volt-amperes from a nameplate.
How to Use It
- Pick the direction you are working in. Turns mode takes the two winding counts and the primary voltage and gives you the secondary voltage. Voltage mode takes the two voltages and the primary turns and gives you the secondary turns required.
- Enter the primary voltage as an RMS value. Nameplate and supply voltages are root mean square, so the answer is too. Mixing a peak value with an RMS one gives an answer wrong by about 1.414.
- Choose how you are describing the load. Resistance, current or volt-amperes. If nothing is connected to the secondary, enter zero and the tool will report the open-circuit case rather than dividing by nothing.
- Read the currents, not just the voltage. The primary current is what the supply, the protective device and the primary conductors have to carry, and it is the number a design turns on.
- Treat the turn count in voltage mode as a starting point. Turns must be whole numbers, and a real winding needs a few per cent more secondary turns than the ideal figure to compensate for the voltage lost in the windings under load.
The Formula and a Worked Example
The turns ratio is a = Np/Ns, the secondary voltage is Vs = Vp/a, the primary current is Ip = Is/a, and the impedance reflected to the primary is Zp = a2Zs.
Work the defaults through. A transformer with 400 primary turns and 40 secondary turns has a ratio of 400 ÷ 40 = 10, so it steps down by ten. On a 240 V primary the secondary sits at 240 ÷ 10 = 24 V. A 6 Ω load across that secondary draws 24 ÷ 6 = 4 A, so the apparent power is 24 × 4 = 96 VA. The primary current is 4 ÷ 10 = 0.4 A, and a quick check confirms the power balance: 240 × 0.4 = 96 VA on the primary side as well. The impedance the primary circuit sees is 102 × 6 = 600 Ω, which is exactly 240 ÷ 0.4. Every one of those numbers is consistent, which is the signature of the ideal model.
Notice how small the primary current is. That asymmetry is the entire reason electricity is transmitted at high voltage: the energy lost heating a conductor goes as the square of the current, so cutting the current by ten cuts the transmission loss by a hundred. The voltage drop calculator shows that effect on a specific cable run.
Impedance Reflection Is the Underrated Result
Most explanations stop at voltage and current. The third consequence is less well known and arguably more useful: a transformer changes the impedance a source sees, by the square of the turns ratio.
This is why an audio output transformer exists. A valve amplifier stage wants to work into several thousand ohms; a loudspeaker is eight ohms, and connecting them directly wastes almost all the available power. A transformer with a ratio of 25:1 makes an 8 Ω speaker look like 252 × 8 = 5,000 Ω to the valve. Nothing about the speaker changed; the transformer changed what the amplifier is looking at.
The same relation explains a failure that puzzles people the first time they meet it. Short the secondary and the reflected impedance goes to zero, so the primary sees a near short circuit. Winding resistance and leakage reactance put a ceiling on the resulting current, but it is still far above the rated value, which is why protection is sized against the primary current the tool reports rather than against the secondary load.
Where the Ideal Model Departs From a Real Transformer
Four effects all push the same way, and none is in the arithmetic above. The first is winding resistance: both windings are wire, and current through wire produces a drop that never reaches the load. This is why a small transformer measured on open circuit reads higher than its nameplate secondary voltage, since the nameplate figure is the voltage at full rated load. A 12 V transformer reading 13.5 V unloaded is behaving correctly.
The second is leakage flux. Not all of the flux produced by the primary links the secondary; some escapes through the air. It appears in the circuit model as a series inductance, contributing a reactive voltage drop that grows with load current.
The third is the magnetising current a real transformer draws even with nothing connected, because it takes current to establish the flux in the core at all. The fourth is core loss: hysteresis as the core is magnetised and demagnetised each cycle, plus eddy currents in the core steel. Both are roughly constant with load, which is why a transformer left energised with nothing connected still gets warm and still costs money to run. Together these effects mean efficiency is high but never unity, and the volt-ampere figures on the two sides are close but not equal.
Why Transformers Are Rated in Volt-Amperes
A transformer nameplate gives volt-amperes, never watts, and the reason is physical. Winding heating depends on the current, and core saturation depends on the applied voltage and frequency. Neither cares about the phase angle between them. A 500 VA transformer is at its thermal limit at 500 VA whether the load is a resistive heater at unity power factor or a motor at 0.7, even though the second is doing only 350 W of useful work.
The boundary in one sentence: this page solves the turns-ratio relation between two windings, while the kVA calculator sizes a rating from a load and converts between kVA, kW and amps. The power factor calculator handles the gap between the two power figures, and the kVA calculator covers the polyphase case, where a star or delta connection puts a factor of the square root of three between the winding ratio and the line-to-line voltage ratio.
Ratings, tappings and connection symbols for power transformers are the subject of an international standard, IEC 60076-1:2011, Power transformers — Part 1: General, which applies to three-phase and single-phase power transformers including auto-transformers, with certain small and special transformers excluded from its scope.
How This Differs From the Adjacent Arb Digital Tools
This calculator answers one question: what does a given winding ratio do to voltage, current and impedance. The Ohm's law calculator relates a single voltage, current and resistance with no transformer involved, and it is what you want once you are on one side of the winding and analysing the circuit there. The electrical power calculator handles real, apparent and reactive power from voltage, current and power factor. The solenoid inductance calculator works from the geometry of a coil to its inductance, which is the property that makes the primary draw a magnetising current at all.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Inverting the ratio — voltage follows the turns and current opposes them, so a step-down transformer steps current up. Writing the ratio the wrong way round is wrong by the square of the ratio once impedance enters.
- Mixing peak and RMS values — supply and nameplate voltages are RMS. An oscilloscope reading is peak unless you ask it otherwise, and the two differ by the square root of two on a sine wave.
- Expecting the unloaded secondary to read the nameplate voltage — it will read higher, because the nameplate figure already has the full-load winding drop subtracted from it.
- Assuming the turns ratio equals the voltage ratio on a three-phase transformer — a star-delta connection introduces a factor of the square root of three between the winding ratio and the line-to-line voltage ratio.
- Treating volt-amperes as watts — they are equal only at unity power factor, and a transformer's rating limit is set by the volt-amperes.
Related Free Tools From Arb Digital
For the rating rather than the ratio, use the kVA calculator, and for the gap between apparent and real power the power factor calculator. The Ohm's law calculator and the electrical power calculator cover the underlying circuit relationships, the kVA calculator handles polyphase supplies, and the voltage drop calculator shows what the current on each side costs you along a cable run. Coil properties are covered by the solenoid inductance calculator, and the full free online tools hub lists everything else.
Frequently Asked Questions
It is the number of primary turns divided by the number of secondary turns. The voltage divides by that ratio and the current multiplies by it, so a transformer with 400 primary and 40 secondary turns has a ratio of ten, steps 240 volts down to 24, and steps the current up by the same factor.
No. A transformer only works because the flux is changing, and the secondary voltage alternates at exactly the frequency of the primary. Changing frequency requires power electronics, not a winding ratio.
Because impedance is voltage divided by current, and the transformer divides the voltage by the ratio while multiplying the current by it. Both effects act in the same direction on the quotient, so the impedance seen at the primary is the load impedance multiplied by the ratio squared.
Because you are almost certainly measuring it with nothing connected. The nameplate secondary voltage is the figure at full rated load, after the voltage lost in the winding resistance has been subtracted. On open circuit there is no load current and therefore no drop.
No. A steady current produces a steady flux, a steady flux induces nothing in the secondary, and the primary winding then behaves as a low-value resistor across the supply. Connecting a mains transformer to a direct-current supply typically destroys it.
Because the limits are thermal and magnetic. Winding heating depends on current and core saturation depends on voltage, and neither depends on the phase angle between them. A transformer reaches its limit at its rated volt-amperes regardless of the load's power factor.
Good enough for arithmetic and teaching, and optimistic for a real device. Winding resistance, leakage flux, magnetising current and core loss all reduce the delivered secondary voltage and the efficiency, and all of them grow in relative importance as the transformer gets smaller.
Switch the tool to voltage mode, enter both voltages and the primary turn count, and it returns the ideal secondary turns. Round up to a whole number and add a small allowance, because a real winding loses some voltage internally under load.
This tool is provided for educational and estimating use only. It uses the ideal transformer model and does not account for winding resistance, leakage reactance, core loss, saturation, insulation rating, temperature rise or any code compliance requirement. It is not electrical design advice. Work on mains or high-voltage equipment must be designed and carried out by a qualified electrician or electrical engineer under the regulations applicable in your jurisdiction.
