TAHA Engineering Toolsby TAHA Knowledge Lab

Electrical Engineering

Transformer Turns Ratio Calculator

Turns ratio, secondary voltage or secondary turns of an ideal transformer.

Inputs

Calculate from
Transformer symbol: primary winding with Np turns and voltage Vp on the left, secondary winding with Ns turns and voltage Vs on the right, separated by an iron core.VpVsPrimary NpSecondary Nscore
Two windings share one iron core. In an ideal transformer, Vp ÷ Vs = Np ÷ Ns: the winding with more turns has the higher voltage, and the lower current. Diagram not to scale.

The voltage applied to the input (primary) winding. For a single-phase transformer, the winding voltage.

Leave empty if not needed. Used to find the ideal primary current.

Result

Secondary voltage (ideal, no load)
11.5
Turns ratio Np : Ns
20: 1
Type
Step-down – secondary voltage is lower

With 1,000 turns on the primary and 50 turns on the secondary (ratio 20 : 1), 230 V in gives about 11.5 V out at no load.

Educational estimate — check the assumptions below.

About this calculator

A transformer changes an AC voltage using two coils (windings) on a shared iron core. In an ideal transformer, the voltage on each winding is proportional to its number of turns: twice as many turns on the secondary gives twice the voltage. Use this calculator to find the secondary voltage from the turns, the number of secondary turns for a voltage you want, or the turns ratio needed between two voltages.

The turns ratio is a property of the windings. The actual output voltage under load is a little lower, because of winding resistance and leakage reactance — this is called voltage regulation.

Formula

Find secondary voltage

Vp ÷ Vs = Np ÷ Ns = a    so   Vs = Vp × Ns ÷ Np

Ip = Is ÷ a   (ideal)

V = winding voltage, N = number of turns, I = current, a = turns ratio, p = primary, s = secondary.

Find secondary turns

Ns = Np × Vs ÷ Vp

Ip = Is × Ns ÷ Np   (ideal)

V = winding voltage, N = number of turns, I = current, p = primary, s = secondary.

Find ratio from voltages

a = Np ÷ Ns = Vp ÷ Vs

a > 1: step-down; a < 1: step-up; a = 1: isolation transformer.

Worked example

  • Secondary voltage: 230 V on a 1000-turn primary with a 50-turn secondary. Ratio = 1000 ÷ 50 = 20 : 1; Vs = 230 ÷ 20 = 11.5 V. If the secondary supplies 10 A, the ideal primary current is 10 ÷ 20 = 0.5 A.
  • Secondary turns: for 24 V from 230 V with 920 primary turns: Ns = 920 × 24 ÷ 230 = 96 turns.
  • Ratio: 11 kV to 433 V: a = 11 000 ÷ 433 = 25.40 : 1 (step-down).

Assumptions and limitations

  • Ideal transformer: no winding resistance, no leakage, no magnetising current and no core losses. Power in equals power out.
  • The ideal secondary voltage is the no-load voltage. Under load, real transformers give a slightly lower voltage; the manufacturer’s data gives the regulation.
  • For a three-phase transformer, the ratio of line voltages also depends on the winding connection (for example delta–star). Use winding (phase) voltages for the turns ratio.
  • The calculator does not check core size, flux density, wire size, insulation or temperature rise.

Safety note

Mains and high-voltage transformers can be lethal. Winding, testing and connecting transformers must be done by a qualified person following the applicable safety rules.

References

  • Ideal transformer relations: Vp/Vs = Np/Ns = Is/Ip (standard electrical engineering texts; IEC 60076 terminology).