Transformer Turns Ratio Calculator
The transformer turns ratio relates the primary and secondary voltages, turns, and currents of an ideal transformer. The fundamental relationship is N1/N2 = V1/V2 = I2/I1, where N1 and N2 are primary and secondary turns, V1 and V2 are primary and secondary voltages, and I1 and I2 are primary and secondary currents. This calculator requires primary voltage (V1) and secondary voltage (V2) to compute the turns ratio. Optionally enter the number of primary turns (N1) to compute secondary turns (N2), and enter primary current (I1) to compute secondary current (I2). The calculator also identifies whether the transformer is step-up (secondary voltage higher than primary) or step-down (secondary voltage lower than primary). The turns ratio formula assumes an ideal transformer. Real transformers are highly efficient (97% to 99.5% for large power transformers) but have small losses from winding resistance, core hysteresis, and eddy currents. For most practical sizing and design work, the ideal transformer model is a valid approximation. Transformers only work with alternating current (AC); they cannot transform DC.
Transformer turns ratio formula
Turns Ratio (a) = N1 / N2 = V1 / V2 = I2 / I1
Secondary Turns: N2 = N1 / a = N1 x (V2 / V1)
Secondary Current: I2 = I1 x a = I1 x (V1 / V2)
Worked example
A transformer with V1 = 240 V, V2 = 120 V, N1 = 1,000 turns, I1 = 5 A:
- Turns ratio = 240 / 120 = 2:1
- This is a step-down transformer (secondary voltage is lower)
- Secondary turns N2 = 1,000 / 2 = 500 turns
- Secondary current I2 = 5 x 2 = 10 A
Note: the secondary current is higher because voltage is lower, conserving apparent power (V1 x I1 = 240 x 5 = 1,200 VA = V2 x I2 = 120 x 10 = 1,200 VA).
Frequently asked questions
What is a transformer turns ratio?
The turns ratio (a) of a transformer is the ratio of the number of turns on the primary winding (N1) to the number of turns on the secondary winding (N2). For an ideal transformer, this ratio equals the ratio of primary voltage to secondary voltage (V1/V2) and also equals the inverse ratio of primary current to secondary current (I2/I1). The turns ratio determines how voltage is stepped up or down between windings.
What is the difference between a step-up and a step-down transformer?
A step-up transformer has more turns on the secondary than the primary (N2 greater than N1), so the secondary voltage is higher than the primary voltage. It is used to raise voltage for long-distance power transmission, reducing current and thus resistive losses. A step-down transformer has fewer turns on the secondary (N2 less than N1), lowering voltage for safe use in homes and equipment. The power grid uses step-up transformers at generating stations and step-down transformers at substations and service entrances.
What is an ideal transformer versus a real transformer?
An ideal transformer assumes 100% efficiency: no core losses (hysteresis and eddy current losses), no winding resistance, no leakage flux, and perfect magnetic coupling. Real transformers have core losses that produce heat in the magnetic core, copper losses (I2R) in the windings, leakage inductance, and magnetising current. High-quality power transformers achieve 97% to 99.5% efficiency. The turns ratio formula (N1/N2 = V1/V2) is a good approximation for real transformers under normal load conditions.
Why do transformers only work on AC?
Transformers rely on electromagnetic induction: a changing magnetic field in the primary winding induces a voltage in the secondary winding. This requires a continuously changing (alternating) current. A steady DC current creates a constant magnetic field, which induces no voltage in the secondary. Applying DC to a transformer primary also has no internal impedance limitation, and the winding resistance alone limits current, often causing overheating and burnout. DC power can be transformed using switching power supplies (which chop DC into high-frequency AC before the transformer stage).
How do I interpret a transformer's nameplate kVA rating?
The kVA rating is the apparent power capacity of the transformer: the product of rated voltage and rated current. It represents the maximum load the transformer can supply without overheating under rated conditions. To find the maximum current at the secondary voltage, divide kVA by the secondary voltage (in kV). For example, a 10 kVA transformer at 240 V secondary can deliver up to 10,000 / 240 = 41.7 A. The kVA rating does not account for load power factor; at unity power factor, kVA equals kW.
Sources
- IEEE Standard C57.12.00-2021: General Requirements for Liquid-Immersed Distribution, Power, and Regulating Transformers.
- National Institute of Standards and Technology (NIST): SI units and electromagnetic definitions, SP 330.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. Ideal transformer model. Real transformers have efficiency losses; consult the manufacturer's datasheet.