Transformer Calculator
Calculate turns ratio, secondary voltage, primary and secondary current, impedance transformation, and efficiency for ideal and real transformers.
Solve For
Common Transformer Types & Ratios
| Application | Primary (V) | Secondary (V) | Turns Ratio |
|---|---|---|---|
| Mains power supply (EU) | 230 V | 12 V | ≈ 19:1 |
| Mains power supply (US) | 120 V | 12 V | 10:1 |
| Grid distribution | 11,000 V | 230 V | ≈ 48:1 |
| Audio output (8 Ω speaker) | 5,000 Ω load | 8 Ω | ≈ 25:1 |
| Doorbell transformer | 120/230 V | 8–24 V | varies |
| Microwave oven HV | 120/230 V | ~2,000 V | ≈ 1:9 step-up |
Frequently Asked Questions
Turns ratio N = Np/Ns. The voltage relationship is Vs/Vp = Ns/Np = 1/N. The current relationship is Is/Ip = Np/Ns = N (ideal transformer). If N > 1, it is a step-down transformer; if N < 1, it is a step-up transformer.
Secondary voltage Vs = Vp × (Ns/Np) = Vp / N. For example, a 230 V primary with a 10:1 turns ratio gives Vs = 230/10 = 23 V. For a step-up transformer with turns ratio 1:10, Vs = 230 × 10 = 2300 V.
A transformer reflects impedance from secondary to primary as: Zp = (Np/Ns)² × Zs = N² × Zs. This is used in impedance matching — for maximum power transfer, source impedance should equal the reflected load impedance. For example, a 100 Ω speaker through a 10:1 transformer appears as 10,000 Ω to the primary circuit.
Transformer efficiency η = (Output power / Input power) × 100% = (Vs × Is) / (Vp × Ip) × 100%. Real transformers have core losses (hysteresis + eddy currents) and copper losses (I²R in windings). Typical large power transformers achieve 95–99% efficiency. Small audio transformers may be 80–95% efficient.
Ideal Transformer Equations
For an ideal (lossless) transformer: Vs/Vp = Ns/Np and Ip/Is = Ns/Np. This means input power equals output power: Vp × Ip = Vs × Is. Step-up in voltage means step-down in current by the same ratio — energy is conserved.
Real Transformer Losses
Real transformers are not perfectly efficient. Core losses (iron losses) occur due to hysteresis (magnetization/demagnetization cycling) and eddy currents (circulating currents in the core). Copper losses (I²R) occur in the primary and secondary windings. Total efficiency: η = Pout/Pin = (Pout)/(Pout + Pcore + Pcopper).
- Turns ratio determines voltage step-up or step-down ratio
- Current is inversely proportional to turns ratio (ideal case)
- Impedance is transformed by the square of the turns ratio
- Auto-transformers use a single tapped winding — more efficient but no isolation