What is the transformer formula?
The ideal transformer equation is Vp ÷ Vs = Np ÷ Ns = Is ÷ Ip: voltage scales with the turns and current scales the other way. With no losses, power in equals power out, so Vp × Ip = Vs × Is.
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Transformer calculator
A transformer calculator for the turns ratio, secondary voltage and current, primary current, VA rating and reflected impedance. Add efficiency and regulation when you are working from a real part rather than the ideal model.
Solve for
Examples
V
Load is given as
A
%
100 % is the ideal transformer.
%
Voltage rise from full load to no load, as % of full load. From the datasheet.
Secondary voltage
12 V
- Turns ratio Np ÷ Ns
- 10
- Type
- Step-down
- Secondary current
- 2 A
- Primary current
- 200 mA ideal
- Load power
- 24 VA
- Primary VA
- 24 VA
- Load impedance
- 6 Ω
- Load seen at the primary
- 600 Ω a² × ZL
- Volts per turn
- 120 mV
Sine waves at the rated frequency. Primary current is the load component at unity power factor; real parts add a magnetizing current, typically 1 to 5 % of rated.
Each side
| Primary | Secondary | |
|---|---|---|
| Voltage | 120 V | 12 V |
| Current | 200 mA | 2 A |
| VA | 24 VA | 24 VA |
| Impedance | 600 Ω | 6 Ω |
How do you calculate a transformer’s secondary voltage and current?
Multiply the primary voltage by Ns ÷ Np, and divide the secondary load’s VA by the primary voltage for the primary current. A 1000:100 transformer on 120 V gives 12 V on the secondary. Loaded with 2 A, it delivers 24 VA and draws 200 mA from the primary.
Ideal transformer equations
The same flux links both windings, so each turn sees the same voltage. With no losses, power in equals power out.
a = Np ÷ Ns = Vp ÷ Vs = Is ÷ Ip
- a
- turns ratio Np ÷ Ns
- Vp, Vs
- primary and secondary RMS voltage
- Ip, Is
- primary and secondary RMS current
Impedance transforms by the square of the turns ratio, because voltage goes up as current goes down:
Zp = a² × ZL a = √(Zs ÷ ZL) to match
- ZL
- load on the secondary
- Zp
- that load as seen at the primary
- Zs
- source impedance to be matched
The VA rating is the same on both sides for the ideal part. Efficiency η scales the primary current:
VA = Vs × Is Ip = Vs × Is ÷ (η × Vp)
Regulation is expressed against the full-load voltage, so the loaded secondary is below the turns-ratio value:
VR% = (Vno-load − Vfull-load) ÷ Vfull-load × 100 Vfull-load = Vno-load ÷ (1 + VR% ÷ 100)
Worked examples
Example 1: 1000 turns to 100 turns on 120 V, 2 A load
The ratio is a = 1000 ÷ 100 = 10, so Vs = 120 ÷ 10 = 12 V. With 2 A on the secondary, the load is 24 VA and 6 Ω, the primary draws 200 mA, and the load looks like 600 Ω from the primary: 120 V ÷ 200 mA gives the same number.
Example 2: 230 V to 24 V, 50 VA, with real-part figures
A 24 V full-load target with 10 % regulation needs 26.4 V at no load, so the ratio is a = 8.712. With 1150 primary turns, the secondary needs 132 turns, which delivers 24 V at load. Full load is 2.08 A on the secondary and, at 90 % efficiency, 242 mA on the primary.
Example 3: matching an 8 Ω speaker to a 3.2 kΩ plate load
a = √(3200 ÷ 8) = 20, so a 20:1 transformer makes the 8 Ω speaker look like 3.2 kΩ to the amplifier.
Transformer turns ratio table: voltage, current and impedance
What a given Np ÷ Ns does to a 120 V primary and a 50 Ω secondary load. For other ratios, use the transformer turns ratio calculator at the top of the page.
| Np ÷ Ns | Secondary from 120 V | Current ratio Is ÷ Ip | Impedance ratio | 50 Ω load seen at primary |
|---|---|---|---|---|
| 100:1 | 1.2 V | 100× | 10000× | 500 kΩ |
| 20:1 | 6 V | 20× | 400× | 20 kΩ |
| 10:1 | 12 V | 10× | 100× | 5 kΩ |
| 5:1 | 24 V | 5× | 25× | 1.25 kΩ |
| 2:1 | 60 V | 2× | 4× | 200 Ω |
| 1:1 | 120 V | 1× | 1× | 50 Ω |
| 1:2 | 240 V | 0.5× | 0.25× | 12.5 Ω |
| 1:10 | 1.2 kV | 0.1× | 0.01× | 500 mΩ |
Transformer current at full load for common mains voltages
Ideal turns ratio and full-load currents for common mains and secondary combinations. The VA rating tab above gives the currents for any other pair of voltages.
| Primary | Secondary | VA | Turns ratio | Secondary current | Primary current |
|---|---|---|---|---|---|
| 120 V | 5 V | 10 | 24:1 | 2 A | 83.3 mA |
| 120 V | 12 V | 24 | 10:1 | 2 A | 200 mA |
| 120 V | 24 V | 48 | 5:1 | 2 A | 400 mA |
| 230 V | 12 V | 24 | 19.17:1 | 2 A | 104 mA |
| 230 V | 24 V | 50 | 9.583:1 | 2.08 A | 217 mA |
| 230 V | 48 V | 100 | 4.792:1 | 2.08 A | 435 mA |
Where the ideal model stops
- Secondary current flows only with a load, but the primary always draws an exciting current to set up the flux. Michigan Tech’s notes put it at about 1 to 5 % of the rated primary current.
- Winding resistance and leakage make the secondary sag under load. The rated voltage of a small mains transformer is often quoted at full load, so with no load it reads higher: take regulation from the datasheet.
- Flux is proportional to voltage ÷ (frequency × turns × core area), so running a 60 Hz design from 50 Hz raises the flux by 20 % and can saturate the core.
- Turns are whole numbers, so a low-turn winding cannot hit an arbitrary ratio. Use more turns or accept the error the calculator reports.
- Rectifier loads draw narrow pulses, so the RMS current is higher than the DC current. Hammond’s guide de-rates a bridge to 0.62 A DC per AC amp, and half-wave to 0.28 A.
- Wideband and RF transformers follow these relations only in band. Mini-Circuits’ AN-20-002 ties the low-frequency loss to the primary inductance and the high-frequency loss to inter-winding capacitance and series inductance.
- Mains transformers are safety-critical. Use parts certified for your isolation class rather than an arbitrary winding.
Glossary
- Turns ratio (a)
- Primary turns divided by secondary turns, equal to Vp ÷ Vs for an ideal transformer.
- Step-down / step-up
- A transformer whose secondary voltage is lower or higher than its primary voltage.
- VA rating
- The apparent power a transformer can deliver: RMS voltage times RMS current.
- Reflected impedance
- A load impedance as seen from the other winding: multiplied by a² toward the primary.
- Regulation
- The change in secondary voltage from no load to full load, as a percentage of the full-load voltage.
- Magnetizing current
- The primary current that sets up the core flux, drawn even with no load.
Related guides
- Power factor calculator: watts, VA and VAR on the AC side.
- RMS calculator: peak and RMS of the secondary voltage.
- Inductive reactance calculator: the reactance of a winding at the mains frequency.
Frequently asked questions
How do you calculate a transformer turns ratio?
Divide the primary turns by the secondary turns, or equivalently the primary voltage by the secondary voltage. The transformer turns ratio formula is a = Np ÷ Ns = Vp ÷ Vs, so a 120 V to 12 V transformer is 10:1, and 230 V to 24 V is 9.583:1.
How does transformer current change from primary to secondary?
Opposite to the voltage. A 10:1 step-down transformer with 2 A in the secondary draws 200 mA from a 120 V primary, ignoring magnetizing current and losses.
What is the reflected impedance formula?
Zp = a² × ZL, where ZL is the load on the secondary and Zp is how it looks from the primary. Through a 10:1 transformer a 6 Ω load looks like 600 Ω.
What turns ratio matches 8 Ω to 3.2 kΩ?
a = √(Zs ÷ ZL) = √(3200 ÷ 8) = 20, a 20:1 output transformer. In general the impedance ratio is the square of the turns ratio.
What is the VA rating of a transformer?
The product of the RMS voltage and the RMS current it can carry. It is in VA and not watts because the winding heating depends on the current regardless of the load’s power factor. Divide VA by the secondary voltage for the full-load secondary current; the VA rating tab does it for you.
How do you calculate transformer size?
Size it by VA: multiply the secondary voltage by the full-load secondary current. A 24 V secondary at 2.08 A needs 50 VA. Allow more for a rectifier load, because its narrow current pulses raise the RMS current above the DC current.
What is transformer voltage regulation?
The rise from full load to no load, as a percentage of the full-load voltage. A secondary of 13.2 V with no load and 12 V at full load has 10 % regulation, so the turns are chosen to give the higher voltage.
Does a transformer work on DC?
No. Induced voltage depends on the rate of change of flux, so steady DC only produces a winding current limited by resistance, and can saturate the core.
What DC current can a transformer supply through a rectifier?
Often less than its AC rating, because capacitor-input loads draw narrow, high-peak pulses. Hammond’s rectifier guide gives 0.62 A DC per AC amp for a bridge, 0.28 A for half-wave and 1.00 A for a center-tap winding.
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Sources
- Rose-Hulman, Electromechanical Devices Lecture 10: Ideal Transformers
- Mini-Circuits AN-20-002, Application Note on Transformers (V, I and Z relations)
- University of Illinois ECE 330 Lecture 7: ideal transformers and impedance matching
- Michigan Tech EET2233 Chapter 5: Transformers (regulation, exciting current)
- Texas Instruments SLUP126, Magnetics Design Handbook Section 4: Power Transformer Design
- Hammond Manufacturing, Design Guide for Rectifier Use (5C007)
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