Calculators

Transformer Turns Ratio Calculator

Calculate transformer turns ratio, secondary turns, current, and reflected impedance.

Calculate an ideal transformer's primary-to-secondary turns ratio from voltage. Optional inputs also estimate secondary turns, ideal secondary current, and secondary load impedance reflected to the primary.

Primary voltage (V)Secondary voltage (V)Primary turns OptionalPrimary current (A) OptionalSecondary load impedance (Ω) Optional

Primary : secondary turns ratio

10 : 1

Ideal step-down transformer

Inverse ratio1 : 10

Estimated secondary turns100 turns

Ideal secondary current5 A

Load reflected to primary800 Ω

Ideal relationship: Np/Ns = Vp/Vs = Is/Ip; a secondary load reflects to the primary as Zp = Zs × (Np/Ns)².

This is an ideal AC transformer model. It does not verify core flux density, frequency suitability, saturation, insulation, winding resistance, leakage reactance, temperature rise, regulation, losses, or safe construction.

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About This Tool

An ideal transformer's voltage change is set by the ratio of turns on its primary and secondary windings. This calculator uses the primary-to-secondary convention a = Np/Ns = Vp/Vs, then optionally applies that same ratio to estimate secondary winding turns, the inverse current relationship, and the impedance of a secondary load as seen from the primary. It is useful for electronics coursework, quick transformer ratio checks, audio impedance examples, and preliminary AC circuit calculations. The calculation runs locally in the browser.

How To Use It

Enter positive primary and secondary AC voltage magnitudes using the same basis, such as RMS-to-RMS.
Read the primary-to-secondary turns ratio and whether the ideal ratio is step-down, step-up, or 1:1 isolation.
Optionally enter primary turns to estimate secondary turns, primary current to estimate ideal secondary current, or secondary load impedance to calculate its reflected primary impedance.
Use the result as an ideal relationship only. Real transformer selection and construction require frequency, core, insulation, thermal, regulation, and safety checks.

Examples

120 V to 12 V step-down

120/12 = 10, so the ideal primary-to-secondary ratio is 10:1. If the primary has 1000 turns, the secondary has about 100 turns.

12 V to 120 V step-up

12/120 = 0.1, so Np/Ns = 0.1 and the secondary has ten times as many turns as the primary in the ideal model.

Reflected 8 Ω load

With a 10:1 primary-to-secondary ratio, an 8 Ω secondary load reflects as 8 × 10² = 800 Ω at the primary in the ideal model.

Useful Notes

Turns and voltage ratio

For an ideal transformer sharing the same changing core flux, Np/Ns = Vp/Vs. This calculator defines a as primary divided by secondary, so a value above 1 corresponds to voltage step-down and a value below 1 to voltage step-up.

Current ratio

Ideal power conservation gives VpIp = VsIs. Combining that with the voltage ratio gives Is = Ip × a. A voltage step-down therefore corresponds to an ideal current step-up, but this does not mean a physical transformer can supply unlimited current.

Reflected impedance

A load connected to the secondary appears at the primary multiplied by the square of the turns ratio: Zp = Zs × a². This relationship is important in impedance matching because even a modest turns ratio can create a much larger impedance transformation.

Ratio convention matters

Some references state transformer ratio as secondary-to-primary instead of primary-to-secondary. Hanakash uses Np:Ns. A 120 V to 12 V transformer is therefore shown as 10:1, while the inverse convention would write 1:10.

Real transformer limitations

Real transformers have winding resistance, leakage inductance, magnetizing current, core losses, finite regulation, insulation constraints, thermal limits, and frequency-dependent saturation risk. Nameplate ratings and manufacturer data take precedence over this ideal calculation.

Use consistent voltage definitions

Compare like with like: RMS with RMS, peak with peak, and the same phase basis on both sides. Mixing line-to-line and line-to-neutral values or loaded and no-load voltages can produce a misleading ratio.

FAQ

What is the transformer turns ratio formula?

Using the primary-to-secondary convention, a = Np/Ns = Vp/Vs. N is winding turns and V is the corresponding ideal winding voltage.

Is 10:1 step-up or step-down?

With this calculator's Np:Ns convention, 10:1 is step-down because the primary has ten times the secondary turns and ideal secondary voltage is one-tenth of primary voltage.

Why does impedance use the ratio squared?

Voltage scales by a while current scales inversely by a. Because impedance is voltage divided by current, the combined transformation is a².

Can this design a mains transformer for me?

No. It provides ideal ratio relationships only and does not validate core size, volts per turn, flux density, insulation, creepage, thermal behavior, protection, or applicable electrical-safety requirements.