Transformer turns equation: Vp/Vs = Np/Ns
Primary p.d. ÷ secondary p.d. = primary turns ÷ secondary turns. In symbols, Vp/Vs = Np/Ns. Vp and Vs are the potential differences across the primary and secondary coils in volts (V). Np and Ns are the numbers of turns on each coil, which have no unit. It is a Higher tier equation in GCSE Physics, and the sheet in your exam prints it.
Equation
Vp ÷ Vs = Np ÷ Ns
| Symbol | Quantity | Unit |
|---|---|---|
Vp | primary potential difference | V |
Vs | secondary potential difference | V |
Np | primary turns | turns |
Ns | secondary turns | turns |
What each specification says
| Exam board | Status | Equation |
|---|---|---|
| AQA Physics (8463) | Given on the sheet · Higher tier only | Vp/Vs = np/ns |
| AQA Combined Science (8464) | Not in this specification | |
| Edexcel Physics (1PH0) | Given on the sheet · Higher tier only | Vp/Vs = Np/Ns |
| Edexcel Combined Science (1SC0) | Not in this specification | |
| OCR Gateway Physics A (J249) | Given on the sheet · Higher tier only | Vp/Vs = Np/Ns |
| OCR Twenty First Century Physics B (J259) | Given on the sheet · Higher tier only | Vp/Vs = Np/Ns |
Calculator: Vp ÷ Vs = Np ÷ Ns
How a transformer works
A transformer has two coils of wire wound on one iron core. An alternating current in the first coil, the primary, makes a magnetic field that keeps changing. The iron carries that field to the second coil, the secondary, and the changing field makes a potential difference there.
The ratio of turns sets the ratio of voltages. A secondary with more turns than the primary gives a bigger voltage. That is a step-up transformer. Fewer turns on the secondary give a smaller voltage, which is a step-down transformer.
It only works with alternating current. A steady direct current makes a field that does not change, so nothing appears across the secondary.
Board forms and tiers
- AQA Physics (8463): Vp/Vs = np/ns, with a lower case n for the turns.
- Edexcel Physics (1PH0): Vp/Vs = Np/Ns.
- OCR Gateway (J249) and OCR Twenty First Century (J259): Vp/Vs = Np/Ns.
Each board marks this as Higher tier and lists it with the equations you select and apply. It belongs to the separate Physics courses, so AQA Combined Science Trilogy (8464) and Edexcel Combined Science (1SC0) do not include it.
For exams in 2025, 2026 and 2027, the boards hand out a sheet with every physics equation, and the sheets continue from 2028. Check your own board on the Edexcel equation list or the full physics equation sheet page.
Transformers in the National Grid
Power stations use step-up transformers to raise the voltage before the electricity sets off along the cables. Near your home, step-down transformers bring it back to 230 V. A phone charger steps it down again to a few volts.
The reason for the high voltage comes from a second transformer equation. For the same power, a higher voltage means a lower current, and a lower current wastes less energy heating the cables. See the transformer power equation and the heating equation P = I²R.
Worked examples
Vs
- Vs = Vp × Ns ÷ Np
- Vs = 230 × 30 ÷ 1150
- Vs = 6900 ÷ 1150
- Vs = 6 V
6 V
Ns
- Change both voltages to volts: 25 kV = 25 000 V and 400 kV = 400 000 V
- Ns = Np × Vs ÷ Vp
- Ns = 500 × 400 000 ÷ 25 000
- Ns = 8000 turns
8000 turns
Np
- Np = Ns × Vp ÷ Vs
- Np = 60 × 230 ÷ 12
- Np = 13 800 ÷ 12
- Np = 1150 turns
1150 turns
Common mistakes
- Turning the ratio upside down on one side only. If Vp is on top on the left, Np must be on top on the right.
- Mixing kilovolts with volts. Write 25 for a primary in kV and 400 000 for a secondary in volts, and the answer is 1000 times out. Put both in the same unit.
- Expecting a step-up transformer to create energy. The voltage goes up, but the current goes down by the same factor.
- Giving the number of turns a unit. A turn count is a plain number.
Solve for Ns or Vp in the Equation Rearranger.
Questions people ask
Why do transformers need an iron core?
Iron is easily magnetised. It guides the changing magnetic field from the primary coil through the secondary coil, so more of it reaches the second coil.
How can I tell step-up from step-down quickly?
Compare the turns. If Ns is bigger than Np, the output voltage is bigger, so it steps up.