Transformer Ratio Formula
Calculate transformer turns ratio Np/Ns = Vp/Vs.
Returns voltage and current transformation for step-up and step-down transformers with power conservation.
Need to calculate, not just reference? Use the interactive version.
Open Transformer Turns Ratio Calculator →
The Formula
V_p / V_s = N_p / N_s = I_s / I_p
A transformer changes voltage levels using electromagnetic induction between two coils. The voltage ratio equals the turns ratio. When voltage goes up, current goes down proportionally.
Variables
| Symbol | Meaning |
|---|---|
| V_p | Primary (input) voltage |
| V_s | Secondary (output) voltage |
| N_p | Number of turns in the primary coil |
| N_s | Number of turns in the secondary coil |
| I_p | Primary (input) current |
| I_s | Secondary (output) current |
Example 1
A transformer has 500 primary turns and 50 secondary turns. Input is 240 V.
V_s = V_p × (N_s / N_p) = 240 × (50 / 500)
V_s = 24 V (step-down transformer, 10:1 ratio)
Example 2
A step-up transformer needs to convert 120 V to 600 V. Primary has 200 turns.
N_s = N_p × (V_s / V_p) = 200 × (600 / 120)
N_s = 1,000 turns needed on the secondary coil
When to Use It
Use the transformer ratio formula when:
- Designing power supplies that convert between voltage levels
- Understanding how electricity is transmitted over long distances
- Selecting the right transformer for a specific application
- Calculating current changes when voltage is stepped up or down
Key Notes
- The formula assumes an ideal transformer (no losses); real transformers are 95–99% efficient, with losses from winding resistance (copper loss) and magnetic hysteresis (core loss) — these produce heat and reduce actual output voltage under load
- Transformers only work with AC — a DC current creates no changing magnetic flux, so no voltage is induced in the secondary; connecting a transformer to DC will overheat and destroy the primary winding
- Impedance transforms as the square of the turns ratio: Z_p/Z_s = (N_p/N_s)² — this is used in audio engineering to match speaker impedance (8 Ω) to amplifier output impedance for maximum power transfer
- The reason electricity is transmitted at high voltage over long distances is the transformer: stepping up voltage reduces current proportionally, and since power loss = I²R, lower current means dramatically less heat lost in transmission lines