About the Transformer Turns Ratio Calculator
This transformer turns ratio calculator works out how an ideal transformer converts voltage, current and impedance. Enter the number of turns on the primary and secondary windings and the primary voltage to get the secondary voltage — or enter the two voltages you want and the primary turns to find how many secondary turns to wind.
Add the resistance of the load connected to the secondary and the calculator also returns the secondary and primary currents, the power transferred and the impedance the load presents to the source (the reflected impedance). That makes it useful for students learning transformer theory, hobbyists rewinding mains or audio transformers, and engineers sizing matching transformers for speakers, RF baluns or instrumentation.
The results assume an ideal transformer: no winding resistance, no core loss, no leakage inductance and a perfectly coupled core, so input power equals output power. Real transformers have efficiencies from about 90% for small units to over 99% for large power transformers, and their secondary voltage sags under load, so treat the figures as the theoretical design target.
With the default inputs, the turns ratio a = np/ns is 10. Change any value above to recalculate instantly.
How to use the transformer turns ratio calculator
- 1Choose whether you know both turn counts or both voltages.
- 2Enter the primary turns and primary voltage.
- 3Enter the secondary turns, or the secondary voltage you need.
- 4Optionally enter the load resistance to get currents, power and reflected impedance.
- 5Read the turns ratio, step-up or step-down type and secondary values.
Formula and method
In an ideal transformer the same magnetic flux links both windings, so each turn carries the same voltage. The voltage ratio therefore equals the turns ratio: Vp/Vs = Np/Ns = a. Because no energy is lost, Vp × Ip = Vs × Is, which means current transforms inversely: Is/Ip = a.
Combining the two gives the impedance relationship Zp = a² × ZL: a load on the secondary appears a² times larger from the primary side. This is why a 10:1 transformer makes an 8 Ω speaker look like 800 Ω to a valve amplifier. The secondary current here is Vs ÷ RL for a resistive load, and the primary current is that divided by a.
- Np, Ns
- Primary and secondary turns
- Vp, Vs
- Primary and secondary voltages (RMS)
- Ip, Is
- Primary and secondary currents
- a
- Turns ratio Np/Ns
- ZL, Zp
- Load impedance and its reflected value on the primary
Worked examples
500:50 step-down from 230 V into a 10 Ω load
a = 500/50 = 10, so the secondary sees 230/10 = 23 V. A 10 Ω load draws 23/10 = 2.3 A, the primary supplies 2.3/10 = 0.23 A, and 23 × 2.3 = 52.9 W passes through. The load looks like 10² × 10 = 1,000 Ω from the mains side.
Designing a 120 V to 12 V transformer with 1,200 primary turns
Ns = 1200 × 12/120 = 120 turns, a 10:1 ratio. A 4 Ω load pulls 12/4 = 3 A from the secondary and 0.3 A from the primary, transferring 36 W; the load reflects as 100 × 4 = 400 Ω.
Step-up: 100 to 2,000 turns from 12 V into 10 kΩ
a = 100/2000 = 0.05 (1:20), so 12 V becomes 240 V. The 10 kΩ load takes 24 mA, which costs 0.48 A on the 12 V side, 5.76 W either way. Seen from the primary the load is only 0.05² × 10,000 = 25 Ω.
Frequently asked questions
How do you calculate the turns ratio of a transformer?+
Divide the primary turns by the secondary turns (a = Np/Ns). If you only know voltages, a = Vp/Vs. A ratio above 1 is a step-down transformer, below 1 is step-up, and exactly 1 is an isolation transformer.
Is the turns ratio the same as the voltage ratio?+
For an ideal transformer, yes: Vp/Vs = Np/Ns. In a real transformer the loaded secondary voltage is slightly lower because of winding resistance and leakage, so manufacturers add a few percent extra secondary turns.
Why does current go up when voltage goes down?+
Energy is conserved. If a transformer halves the voltage, it must double the current to deliver the same power (ignoring losses), so Is/Ip equals the turns ratio Np/Ns.
What is reflected impedance?+
It is how a load on the secondary looks from the primary side. It scales with the square of the turns ratio, Zp = (Np/Ns)² × ZL, which is the principle behind audio output transformers and RF impedance matching.
Can a transformer work on DC?+
No. A transformer needs a changing magnetic flux, which only alternating current (or pulsed DC) provides. Steady DC produces no secondary voltage and can saturate the core and overheat the primary winding.