Library / Electrical / ELE-15
Electrical
Transformer equation
Secondary voltage of an ideal transformer from the primary voltage and the turns on each winding.
- Ref
- ELE-15
- Rev
- v1
- Field
- Electrical
- Result
- Vs [V]
Subscripts p and s mean primary and secondary. V is voltage, N the number of turns and I the current. The calculator gives Vs = Vp × Ns / Np.
The voltage across each winding is proportional to its number of turns, so a secondary with fewer turns steps the voltage down. An ideal transformer wastes nothing, so power in equals power out, and the current changes in the opposite sense to the voltage.
Calculator
- Turns ratio Np/Ns19.17 ×
- Voltage ratio Vs/Vp0.05217 ×
- Current ratio Is/Ip (ideal)19.17 ×
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- Voltage scales with the turns ratio and current scales inversely, so the product V × I is the same on both sides of an ideal transformer.
- Primary and secondary turns act in opposite ways: Vs is proportional to Ns and inversely proportional to Np.
- Real transformers lose a few percent as heat in the windings and core, so the secondary voltage under load is a little below the ideal value and the primary current a little above the ideal ratio.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (V) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Np Primary turns | 50 to 5,000 turns | 2.76 | 276 | 273.2 | +10% | −9.09 % |
| Ns Secondary turns | 10 to 1,000 turns | 2 | 200 | 198 | +10% | +10 % |
| Vp Primary voltage | 12 to 400 V | 0.6261 | 20.87 | 20.24 | +10% | +10 % |
Sweep of Secondary turns
| Secondary turns (turns) | Secondary voltage (V) |
|---|---|
| 10 | 2 |
| 17.78 | 3.557 |
| 31.62 | 6.325 |
| 56.23 | 11.25 |
| 100 | 20 |
| 177.8 | 35.57 |
| 316.2 | 63.25 |
| 562.3 | 112.5 |
| 1,000 | 200 |
Sweep one variable
Variables and how each one contributes
Secondary voltage
What the equation gives you. Everything else feeds it.
Primary voltage
RMS voltage applied to the primary winding. Directly proportional: the secondary voltage follows the primary at a fixed turns ratio.
Primary turns
Number of turns on the primary winding. Inversely proportional: more primary turns for the same primary voltage lowers the secondary voltage.
Secondary turns
Number of turns on the secondary winding. Directly proportional: more secondary turns raise the secondary voltage.
Worked example with the values above
- Turns ratio: Ns/Np = 60 / 1,150 = 0.05217.
- Vs = Vp × Ns/Np = 230 × 0.05217 = 12 V.
- For an ideal transformer the current ratio is the inverse, Is/Ip = Np/Ns = 19.17. A secondary supplying 1 A therefore draws about 52.17 mA from the primary.
Assumptions and limits
- Ideal transformer: no winding resistance, no leakage flux and no core losses, so Pp = Ps.
- Sinusoidal AC at constant frequency. A transformer does not work with steady DC.
- Voltages are all RMS values (or all peak values).
Common mistakes
- Inverting the ratio. The voltage ratio uses Ns over Np, but the current ratio uses Np over Ns.
- Trying to use a transformer on DC.
- Treating the loaded secondary voltage as equal to the ideal no-load value.
Statistics and uncertainty
Turns counts are exact integers, so the ideal ratio is exact. The uncertainty comes from the real device and the supply. Voltage regulation (the drop from no-load to full-load secondary voltage) is typically a few percent for small mains transformers, and the supply voltage itself is typically allowed to vary by about ±10% around nominal.
Where it is used
- Stepping mains voltage down for electronics and chargers.
- Stepping voltage up for transmission, to cut I²R loss.
- Isolating a circuit from the supply.
Maths you need
- Ratios: voltage and turns are in proportion
- Power: Pp = Ps means VpIp = VsIs