Calculation
ü = U1/U2 = N1/N2
Fewer secondary turns mean lower voltage and ideally higher current.
U1/U2 = N1/N2
Transformer Turns Ratio Calculator
Fewer secondary turns mean lower voltage and ideally higher current.
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Secondary voltage U2 — The voltage at the transformer's secondary (output) side under unloaded, ideal operation. As a result it follows from U1/ü.
- Primary voltage U1 — The voltage applied to the primary (input) side. Source: mains voltage or the nameplate.
- Turns ratio ü — The turns ratio ü = U1/U2 = N1/N2 (ratio of primary to secondary winding turns N). Source: the transformer's nameplate, or computed from the winding counts.
Example
230 V / 24 V gives ü ≈ 9.58.
Assumptions and limits
Ideal transformer without copper, core or leakage losses.
Understand Transformer Turns Ratio Calculator
This calculator finds the missing quantity among primary voltage U1, secondary voltage U2 and turns ratio ü from the other two, for an ideal transformer. It explains why real transformers, despite this simple turns-ratio relationship, always have an efficiency below 100%.
What does this quantity describe?
For an ideal transformer, the voltage ratio equals the turns ratio: ü = U1/U2 = N1/N2. A higher turns count on the primary side means a correspondingly lower secondary voltage.
A transformer works like a mechanical gearbox for electrical energy: just as a gear pair trades speed for torque, a transformer trades voltage for current. Under ideal, loss-free transfer, current on the higher-voltage side falls by the same ratio that voltage rises.
Formula and variables
ü = U1/U2 = N1/N2
ü = U1/U2 = N1/N2U2 = U1/üU1 = U2 · ü
| Symbol / input | Meaning |
|---|---|
| Secondary voltage U2 | The voltage at the transformer's secondary (output) side under unloaded, ideal operation. As a result it follows from U1/ü. |
| Primary voltage U1 | The voltage applied to the primary (input) side. Source: mains voltage or the nameplate. |
| Turns ratio ü | The turns ratio ü = U1/U2 = N1/N2 (ratio of primary to secondary winding turns N). Source: the transformer's nameplate, or computed from the winding counts. |
Choose the inputs correctly
Enter two of the three quantities. Turns ratio requires both voltages, secondary voltage requires primary voltage and ratio, primary voltage requires secondary voltage and ratio. The formula applies to the no-load voltage with no connected load.
How to use the calculator
Select the target quantity and enter the two known values with units. Keep in mind that real transformers deliver a somewhat lower secondary voltage under load than the ideal no-load value calculated here.
Worked example
Given U1 = 230 V and U2 = 24 V, substitution gives ü = 230/24 ≈ 9.58.
Understand the result and units
A ratio of ü ≈ 9.58 means the primary winding has about 9.58 times as many turns as the secondary. Under ideal, loss-free transfer, secondary current would correspondingly be about 9.58 times the primary current.
Voltages are given in volts (V); turns ratio ü is a dimensionless ratio. Turn counts N1 and N2 are also dimensionless and integer.
Why do real transformers have an efficiency below 100%?
Real transformers lose part of the transferred power to two effects: copper losses occur in the ohmic resistance of the windings and grow with the square of load current; they are negligible at low load but dominate at full load. Iron (core) losses occur from remagnetisation and eddy currents in the transformer core and occur already at no load, nearly independent of load. For household to medium-size transformers, full-load efficiency typically runs between 95% and 98.5%.
Typical applications
Transformer ratios are used to design power supplies, safety extra-low-voltage transformers, doorbell and control transformers, and to match voltage between distribution grid and load.
Assumptions, limits and common mistakes
The formula describes the ideal, loss-free transformer at no load. Real transformers additionally have copper losses (in the windings, dependent on load current) and iron losses (in the core, nearly load-independent), so actual secondary voltage under load falls somewhat below the ideal value. Typical full-load efficiency runs about 95-98.5% depending on size.
Common mistake: Do not confuse the ideal ratio formula with the power balance: for a loss-free transformer, U1·I1 = U2·I2, so current on the high-voltage side falls by the same ratio that voltage rises. Also, do not use the no-load voltage uncritically as the actual voltage under full load.
Frequently asked questions
Why is real secondary voltage under load lower than the calculated no-load value?
Because the windings' internal resistance causes a voltage drop under load, which the ideal no-load formula does not account for.
Does current automatically rise when voltage falls?
For ideal, loss-free transfer, yes: U1·I1 = U2·I2 holds, so a voltage drop by factor ü means a current rise by the same factor.
How efficient is a typical transformer?
Usually between 95% and 98.5% depending on size and loading, with larger power transformers tending toward higher efficiency.