Transformer Turns Ratio Calculator Formula

Understand the math behind the transformer turns ratio calculator. Each variable explained with a worked example.

Use the Transformer Turns Ratio Calculator

Formulas Used

Turns Ratio (Np:Ns)

ratio = turns_ratio

Primary Current

i_primary = power_va / v_primary

Secondary Current

i_secondary = power_va / v_secondary

Power Loss

power_loss = power_va * (1 - efficiency_pct / 100)

Output Power

output_power = power_va * efficiency_pct / 100

Variables

VariableDescriptionDefault
v_primaryPrimary Voltage(V)480
v_secondaryDesired Secondary Voltage(V)120
power_vaTransformer Rating(VA)5000
efficiency_pctEfficiency(%)95
turns_ratioDerived value= v_primary / v_secondarycalculated

How It Works

Transformer Turns Ratio

The turns ratio determines the voltage transformation between primary and secondary windings.

Formulas

Turns Ratio = Vp / Vs = Np / Ns

Ip = VA / Vp and Is = VA / Vs

Current transforms inversely: higher voltage means lower current, preserving power (minus losses).

Power Loss = VA x (1 - Efficiency)

Typical transformer efficiencies range from 90% (small) to 99% (large utility).

Worked Example

480 V to 120 V step-down, 5 kVA, 95% efficient.

v_primary = 480v_secondary = 120power_va = 5000efficiency_pct = 95
  1. 01Turns ratio: 480 / 120 = 4.00:1
  2. 02Primary current: 5000 / 480 = 10.42 A
  3. 03Secondary current: 5000 / 120 = 41.67 A
  4. 04Power loss: 5000 x 0.05 = 250 W
  5. 05Output power: 5000 x 0.95 = 4,750 W

Ready to run the numbers?

Open Transformer Turns Ratio Calculator