Calcylator
Transformer secondary voltage

Transformer secondary voltage:
formula and worked example

The secondary voltage is the primary voltage scaled by the turns, and it sags a little the moment you actually draw current.

Calcylator Editorial Team

Updated · 5 min read

What fixes the secondary voltage

A transformer's secondary voltage is a fixed proportion of the voltage applied to the primary. The proportion is set by the winding turns, not by the load or the size of the core. Put 230 V on a primary that has ten times as many turns as the secondary and the secondary will present about 23 V.

The reason is that both windings are linked by the same alternating flux, so every turn has the same voltage across it. The secondary voltage is then the volts-per-turn figure multiplied by its own turn count.

  • Primary v: the AC voltage applied to the primary, in volts.
  • Primary turns and secondary turns: the number of turns on each winding.
  • Result: ideal secondary voltage, in volts, with the secondary unloaded.

The formula, built from volts per turn

Transformer secondary voltage =primary_v × secondary_turns ÷ primary_turns
primary_v:
Primary v
primary_turns:
Primary turns
secondary_turns:
Secondary turns
Result in volts. It is the ideal, no-load secondary voltage; real windings drop some voltage under load.

A useful way to read this is in two steps. First compute the volts per turn, which is the primary voltage divided by the primary turns. Then multiply by the number of secondary turns. For this transformer, each turn carries 0.23 V and the secondary has 100 of them.

The formula is the turns ratio rearranged, so it holds for step-down and step-up units alike. The only requirement is that the supply is AC, and that the frequency is within what the core was designed for.

Worked example: 230 V, 1,000 to 100 turns

A bell transformer has 1,000 primary turns and 100 secondary turns, fed from 230 V mains. What is the secondary voltage?

  1. Volts per turn: 230 ÷ 1,000 = 0.23 V per turn.
  2. Multiply by secondary turns: 0.23 × 100 = 23 V.
  3. Check with the ratio: 1,000 ÷ 100 = 10, and 230 ÷ 10 = 23 V.

  • Primary v

    230

  • Primary turns

    1,000

  • Secondary turns

    100

Transformer secondary voltage

23 V

Worked from the inputs shown: 230 V on 1,000 primary turns feeding a 100-turn secondary.

If the secondary feeds a 2 A load, it delivers 46 W, and the primary takes about 46 ÷ 230 = 0.2 A, ignoring losses and magnetising current.

No-load figure versus the loaded reality

The formula describes an ideal transformer. In a real one, winding resistance and leakage inductance drop some voltage as current flows, so the loaded secondary is lower than the calculated figure. Small transformers are the most affected, because their windings are thin and relatively resistive.

  • No-load voltage: close to the formula, often slightly above the nameplate rating on small units.
  • Full-load voltage: the figure the manufacturer rates, typically a few percent below no-load for larger transformers and more for small ones.
  • Regulation: the percentage difference between the two, a datasheet figure that varies by size and design.

For a design check, compare the formula's output with the stated rated secondary voltage. A large gap suggests either different turns than you assumed or a transformer designed to deliver its rating at full load.

Supply voltage changes carry straight through

The secondary follows the primary proportionally, so a supply that is 10% high delivers a secondary 10% high: 230 V becomes 253 V and the 23 V output becomes 25.3 V. Mains voltage can vary by several percent across a day, and the secondary variation is the same.

Secondary voltage when only the primary voltage changes by 10%
ScenarioPrimary vCalculated result
Original assumptions23023 V
Primary v increased by 10%25325.3 V

This is a significant point when the secondary feeds a regulator or a rectifier. A rectified and filtered output approaches the peak of the AC voltage, about 1.41 times the RMS value, so a 25.3 V secondary can give over 35 V of DC before any load drops it.

Mistakes with secondary voltage

  • Swapping the turns in the formula, which inverts the answer and gives 2,300 V instead of 23 V.
  • Treating the nameplate voltage and the calculated no-load voltage as interchangeable.
  • Forgetting that the result is an RMS value, so peak voltage is about 41% higher.
  • Connecting the primary to a supply of different frequency, which can saturate the core and overheat the transformer.

A scenario: choosing between taps

A transformer has a 1,000-turn primary and secondary taps at 90 and 100 turns. On a 230 V supply the taps give 20.7 V and 23 V. If the load needs at least 22 V under load and the transformer sags by about 5%, the 23 V tap loaded gives roughly 21.9 V, just below target.

A designer would pick a tap with more turns or specify a transformer with a higher nominal secondary. The check takes a minute and prevents a lamp or relay that never quite behaves.

Common questions

How do I calculate the secondary voltage of a transformer?

Multiply the primary voltage by the secondary turns and divide by the primary turns. For 230 V, 1,000 primary turns and 100 secondary turns, the result is 230 × 100 ÷ 1,000 = 23 V.

Why is my measured secondary voltage different from the calculation?

The formula gives the ideal no-load voltage. Under load, winding resistance causes a drop, and with an unloaded small transformer the reading can be higher than the nameplate. Mains supply variation also changes it proportionally.

Does the secondary voltage depend on the load?

Ideally no, but in a real transformer it does. As the load current rises, resistive and leakage losses in the windings lower the output. The datasheet's regulation figure describes how much it falls between no load and full load.

What is the volts-per-turn of a transformer?

It is the primary voltage divided by the number of primary turns, and it is the same for every turn on the core. The secondary voltage is simply that figure multiplied by the secondary turns.

Can I run a 50 Hz transformer on 60 Hz?

Usually yes, as the lower flux at 60 Hz is gentler on the core. The reverse, running a 60 Hz transformer on 50 Hz, can saturate the core and overheat it. Check the rating on the nameplate.

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