Transformer turns ratio:
formula and worked example

What the turns ratio tells you

A transformer moves energy between two windings sharing a magnetic core. The turns ratio is the number of turns on the primary winding divided by the number on the secondary winding. It is the single number that fixes how the transformer rescales voltage and current.

A ratio above one means more turns on the primary than the secondary, so the secondary voltage is lower, a step-down transformer. A ratio below one is a step-up. A ratio of exactly one gives an isolating transformer, whose job is separation, not voltage change.

• Primary turns: the number of turns on the winding connected to the source.
• Secondary turns: the number of turns on the winding feeding the load.
• Result: a dimensionless ratio, often written in the form 5:1.

The formula and what the ratio controls

For an ideal transformer, the voltage ratio equals the turns ratio, and the current ratio is its inverse. Written in words, primary voltage over secondary voltage equals primary turns over secondary turns, and primary current over secondary current is the same ratio flipped.

Power in is the product of voltage and current, and the two changes cancel, so an ideal transformer delivers the same power it receives. Real ones lose a few percent as heat in the windings and the core.

Worked example: 1,200 turns to 240 turns

A small transformer has 1,200 turns on the primary and 240 turns on the secondary. What ratio is that, and what does it do to a 230 V supply?

1. 1Divide primary by secondary turns: 1,200 ÷ 240 = 5.
2. 2Apply to voltage: 230 V ÷ 5 = 46 V on the secondary.
3. 3Apply to current: if the secondary carries 2 A, the primary draws about 2 ÷ 5 = 0.4 A.

Written as a ratio this is 5:1. The secondary has one fifth of the turns, so it has one fifth of the voltage, and it can supply five times the current the primary takes in.

Using the ratio in practice

The ratio is the first thing you compute when you need to match a transformer to a job. If you know the supply and the voltage you need, the required ratio is their quotient, and the winding data follow from that.

• Step-down: ratio above 1, used for power adapters, door bells and control supplies.
• Step-up: ratio below 1, used in test equipment and to raise voltage for transmission.
• Matching: impedance seen from the primary is the load's impedance multiplied by the square of the ratio, which is why audio transformers are specified by ratio.

The ratio assumes the stated turns are those actually wound. A printed 'rated' ratio may differ slightly from the turns ratio, because manufacturers compensate for winding losses so that the loaded voltage hits the rating.

How changing the turns shifts the ratio

Adding 10% to the primary turns, from 1,200 to 1,320, raises the ratio from 5 to 5.5, and the secondary voltage from the same supply falls by about 9.1%, to 41.8 V. With more primary turns, each turn carries a smaller share of the supply voltage, so every secondary turn delivers less.

Because the ratio is linear in each turns count, there is no surprise in the other direction: a 10% increase in secondary turns lowers the ratio by about 9.1%, which raises the secondary voltage by 10%. Tap changers on a winding use exactly this mechanism to trim output voltage.

Mistakes with turns ratios

• Inverting the ratio: 5:1 is step-down, and reading it as 1:5 gives 1,150 V on a 230 V supply.
• Treating the ratio as a power gain; the current changes oppositely, so power is conserved apart from losses.
• Applying it to a DC supply, where a transformer does not work at all because there is no changing flux.
• Assuming the ideal result under load, when winding resistance and leakage make the real secondary voltage lower.

A scenario: sizing a control transformer

A control panel needs 24 V from a 230 V supply. The ratio required is 230 ÷ 24 ≈ 9.6, so a nominal 10:1 ratio is the nearest practical choice and gives 23 V. If the panel draws 1 A at 24 V, the primary side draws roughly 0.1 A, so the supply wiring is lightly loaded.

This is also a quick check on whether a transformer is oversize: its primary current at no load is only a small magnetising current, and the secondary current times the inverse ratio gives the extra current under load.