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Transformer turns ratio calculator
Electricity
The voltages across the coils of a transformer are in the same ratio as the numbers of turns.
Vp / Vs = Np / Ns
This free calculator is for GCSE and A-level physics. Choose the quantity you want to find, enter the other values with their units, and it shows the working in the layout used in exams, with the answer to the number of significant figures you choose. The values shown are an example. Change them to your own.
Quantity to find
Working
- Write the equationVp / Vs = Np / Ns
- Rearrange to make Vs the subjectVs = Vp Ns / Np
- Substitute the valuesVs = 230 × 50 ÷ 1000
- CalculateVs = 11.5 V
- Give the answer to 3 significant figuresVs = 11.5 V
Worked example
Find Vs, the secondary voltage. Given: primary voltage Vp = 230 V; turns on the primary coil Np = 1000; turns on the secondary coil Ns = 50.0.
- Write the equationVp / Vs = Np / Ns
- Rearrange to make Vs the subjectVs = Vp Ns / Np
- Substitute the valuesVs = 230 × 50 ÷ 1000
- CalculateVs = 11.5 V
- Give the answer to 3 significant figuresVs = 11.5 V
Symbols and units
| Symbol | Quantity | SI unit |
|---|---|---|
| Vp | Primary voltage | V |
| Vs | Secondary voltage | V |
| Np | Turns on the primary coil | no unit |
| Ns | Turns on the secondary coil | no unit |
Transformer turns ratio: rearranged
- To find primary voltage: Vp = Vs Np / Ns
- To find secondary voltage: Vs = Vp Ns / Np
- To find turns on the primary coil: Np = Vp Ns / Vs
- To find turns on the secondary coil: Ns = Vs Np / Vp
Exam tip
A step-up transformer has more turns on the secondary coil. Take care to match each voltage to its own coil.
Common questions
What is the formula for transformer turns ratio?
The equation is Vp / Vs = Np / Ns, where Vp is the primary voltage (V); Vs is the secondary voltage (V); Np is the turns on the primary coil; Ns is the turns on the secondary coil.
What units should I use for transformer turns ratio?
In SI units: primary voltage in V, secondary voltage in V, turns on the primary coil in no unit (a ratio), turns on the secondary coil in no unit (a ratio). The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.
How do I rearrange Vp / Vs = Np / Ns?
Rearranging gives these forms: to find primary voltage: Vp = Vs Np / Ns. to find secondary voltage: Vs = Vp Ns / Np. to find turns on the primary coil: Np = Vp Ns / Vs. to find turns on the secondary coil: Ns = Vs Np / Vp.
Practise transformer turns ratio questions
Press the button for a question with random numbers. Work it out on paper first, then type your answer.
Related
Read the full explanation on the Transformer equation formula page. More electricity equations: Charge, current and time, Ohm’s law, Electrical power, Electrical power, Energy transferred, Resistors in series, Resistors in parallel, Resistivity. See the full list on the physics equation calculator page.