Transformer Ratio Calculator
An ideal transformer relates its two windings by a single turns ratio a = Np / Ns.
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How to use this calculator
- Enter the primary voltage Vp and the secondary voltage Vs (the two rated voltages on the transformer nameplate).
- Optionally enter the primary current Ip to get the ideal secondary current.
- Read the turns ratio, voltage ratio, impedance ratio and whether it is a step-up or step-down transformer.
How it works
An ideal transformer relates its two windings by a single turns ratio a = Np / Ns. Because the same changing flux links both windings, the voltages follow the same ratio: Vp / Vs = Np / Ns = a. When a > 1 the secondary voltage is lower than the primary (step-down); when a < 1 it is higher (step-up); a = 1 is an isolation transformer.
Conservation of power in a lossless transformer (Vp × Ip = Vs × Is) makes the currents transform inversely: Is / Ip = Vp / Vs = a. Reflected impedance transforms with the square of the ratio, Zp / Zs = a², which is why transformers are used for impedance matching. This calculator uses these ideal relationships and ignores winding resistance, leakage and core losses.
Worked example
240 V to 12 V step-down transformer. A mains transformer drops 240 V primary to 12 V secondary. Turns ratio a = Vp / Vs = 240 / 12 = 20, so the winding ratio is 20 : 1 and it is a step-down transformer. The impedance ratio is a² = 400 : 1. If the primary draws 0.5 A, the ideal secondary current is Is = Ip × a = 0.5 × 20 = 10 A.
Common mistakes
- Inverting the ratio. The turns/voltage ratio is primary over secondary (Vp / Vs). A 240→12 V transformer is 20 : 1, not 1 : 20.
- Squaring the wrong quantity for impedance. Impedance transforms as the square of the turns ratio (a²), not linearly like voltage.
- Expecting the secondary current to be lower on a step-down transformer. Voltage steps down but current steps up in the same ratio, since power is conserved.
Frequently asked questions
What is the turns ratio of a transformer?
The turns ratio is the number of primary winding turns divided by the number of secondary turns (Np / Ns). It equals the voltage ratio Vp / Vs, so you can find it from the two rated voltages even without knowing the actual turn counts.
How does current change through a transformer?
For an ideal (lossless) transformer, power in equals power out, so Vp × Ip = Vs × Is. This means current transforms inversely to voltage: a step-down transformer that halves the voltage doubles the available current, and vice-versa.
Why is the impedance ratio the square of the turns ratio?
Impedance seen from the primary is reflected voltage over reflected current. Voltage scales by a and current scales by 1/a, so their ratio scales by a × a = a². This is the basis of transformer impedance matching.
Does this account for real transformer losses?
No. It uses the ideal transformer model and ignores winding resistance, leakage inductance and core (iron) losses. Real transformers have an efficiency typically around 95–99%, so actual secondary voltage under load is a little lower than the ideal figure.
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