What is the transformer turns ratio formula?

The turns ratio is a = N₁ / N₂, where N₁ is the number of primary winding turns and N₂ is the number of secondary winding turns. The voltage ratio matches the turns ratio (V₁/V₂ = N₁/N₂), while the current ratio is the inverse (I₁/I₂ = N₂/N₁), so a step-down transformer that halves the voltage doubles the available current.

How do I calculate secondary voltage from the turns ratio?

Rearrange the voltage equation: V₂ = V₁ × (N₂ / N₁). For example, a transformer with N₁ = 500 turns and N₂ = 100 turns connected to a 230 V primary gives V₂ = 230 × (100/500) = 46 V on the secondary. This is a step-down transformer with a turns ratio of 5:1.

What is reflected impedance and why does it matter?

When a load Z_load is connected to the secondary, the primary "sees" an impedance of Z₁ = a² × Z_load, where a is the turns ratio. This is crucial for impedance matching — in audio amplifiers, for example, an output transformer with the right turns ratio matches a high-impedance amplifier output to a low-impedance loudspeaker, maximising power transfer.

How does transformer efficiency affect the secondary current?

In an ideal transformer, input power equals output power exactly: P_out = P_in. Real transformers suffer copper losses (I²R in the windings) and core losses (hysteresis and eddy currents in the iron). The efficiency η (typically 95–99 % for well-designed power transformers) means P_out = η × P_in, so the secondary current I₂ = (η × V₁ × I₁) / V₂ is slightly less than the theoretical ideal.

How many secondary turns do I need for a target voltage?

Use the winding-design mode and enter the primary turns N₁, primary voltage V₁ and your desired secondary voltage V₂. The calculator solves N₂ = N₁ × (V₂ / V₁). Because the result may not be a whole number, round to the nearest integer and verify the actual output voltage on a prototype before final assembly.

What is the difference between a step-up and step-down transformer?

A step-up transformer has N₂ > N₁ (turns ratio a 1), reducing voltage to safe levels for home appliances. Both obey the same turns ratio equations; the direction of energy transfer depends only on which winding you drive.

Transformer Turns Ratio Calculator

A transformer turns ratio calculator that finds secondary voltage, secondary current, reflected load impedance and apparent power from the winding turns and primary conditions — or works backwards to compute how many turns you need for a desired output voltage. All three modes show full step-by-step working so you can follow exactly how each result is derived.

How it works

An ideal transformer obeys three fundamental equations that all flow from the same physical principle: energy conservation combined with magnetic flux linkage through a shared core.

Voltage ratio — the EMF induced in each winding is proportional to its number of turns:

V₁ / V₂ = N₁ / N₂

so the secondary voltage is V₂ = V₁ × (N₂ / N₁).

Current ratio — because power is conserved (V₁I₁ = V₂I₂ in the ideal case), the currents scale inversely to the voltages:

I₁ / I₂ = N₂ / N₁

A step-down winding that halves the voltage therefore doubles the available current.

Impedance transformation — a load impedance Z_load on the secondary appears to the primary source as a reflected impedance:

Z₁ = a² × Z_load, where a = N₁ / N₂

This quadratic scaling makes transformers essential for impedance matching — connecting a high-impedance source to a low-impedance load without wasting power.

Efficiency — real transformers lose power as heat in the copper windings (I²R losses) and in the iron core (hysteresis and eddy-current losses). The calculator applies an efficiency η so that output apparent power S₂ = η × S₁, and uses that reduced power to compute the actual secondary current.

Worked example

A 230 V mains transformer has 500 primary turns and 100 secondary turns, drawing 1 A primary current at 98 % efficiency, with a 50 Ω load on the secondary:

Turns ratio: a = 500 / 100 = 5 : 1 (step-down)
Secondary voltage: V₂ = 230 / 5 = 46 V
Primary apparent power: S₁ = 230 × 1 = 230 VA
Output apparent power: S₂ = 0.98 × 230 = 225.4 VA
Secondary current: I₂ = 225.4 / 46 = 4.9 A
Reflected impedance: Z₁ = 5² × 50 = 1,250 Ω

The primary source therefore sees a 1,250 Ω load rather than 50 Ω — useful for matching amplifier output stages to loudspeakers or antenna systems.

N₁	N₂	a	V₁	V₂
500	100	5:1	230 V	46 V
200	400	1:2	120 V	240 V
1000	50	20:1	11 kV	550 V
300	300	1:1	230 V	230 V

Every calculation runs entirely in your browser — no values are uploaded or stored.

Formula note

The turns ratio a = N₁/N₂ is the single number from which every transformer property follows. A step-down transformer has a > 1 (more primary turns than secondary), while a step-up transformer has a < 1. An isolation transformer with a = 1 passes voltage unchanged but breaks the galvanic connection between primary and secondary circuits, which is why they appear in medical and audio equipment. The impedance transformation scales as a² — so a 10:1 turns ratio reflects a 50 Ω load as 5,000 Ω; a 2:1 ratio reflects it as 200 Ω. This squared relationship is what makes transformer-based impedance matching so powerful: small changes in turns ratio produce large changes in the reflected impedance seen by the source.