Transformer Turns Ratio Calculator

Primary V + secondary V → turns ratio. Also computes secondary current and reflected impedance.

Result

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How to use this calculator

Enter primary and secondary voltages.
Optionally enter primary current to see the ideal secondary current.
Optionally enter secondary load impedance to see the reflected primary impedance.

About this calculator

An ideal transformer obeys Vp/Vs = Np/Ns and Ip/Is = Ns/Np = 1/n, with power conserved: Vp·Ip = Vs·Is. The same physical relationship makes impedances reflect between the primary and secondary sides scaled by n²: a load Zl on the secondary appears as n²·Zl on the primary. Real transformers have ~95-99% efficiency and additional leakage inductance, but for sizing and matching purposes the ideal-transformer equations are accurate within a few percent.

What this calculator does

This calculator reports the turns ratio n = Np/Ns = Vp/Vs of an ideal transformer along with the secondary current that the ideal-transformer current law (Is = Ip · n) predicts, and the impedance reflected from secondary to primary (Z_primary = n² · Zl). It also cross-checks by computing Is from Vs/Zl and the corresponding Ip — useful for sizing the primary fuse or breaker on a known secondary load.

How it works — the formula

Np / Ns = Vp / Vs = n
Is / Ip = n (ideal)
Z_primary = n² · Z_secondary
P_in = P_out (ideal):  Vp · Ip = Vs · Is

Faraday's law gives Vp/Vs = Np/Ns for the voltage relationship. Energy conservation (P_in = P_out for an ideal transformer) gives the inverse current relationship. The impedance-reflection identity follows directly: Z = V/I, so Z scales by n × n = n² when both V and I change by factors of n in opposite directions.

Sources: IEC 60076-1 — Power transformers, general specifications · IEEE Std C57.12.00-2021 — General Requirements for Liquid-Immersed Distribution, Power, and Regulating Transformers · Sears, Zemansky, Young — University Physics, Ch. 31 (transformers and Faraday's law)

Worked examples

Example 1

120 V → 12 V mains-to-low-voltage

Inputs:: Vp=120, Vs=12, Ip=0.5, Zl=8
Output:: n = 10:1; Is = 5 A; Z_primary = 800 Ω

Classic step-down for low-voltage lighting.

Example 2

6 V battery to 120 V inverter front-end

Inputs:: Vp=6, Vs=120, Ip=20, Zl=240
Output:: n = 0.05 (1:20); Is = 1 A; Z_primary = 0.6 Ω

Step-up — primary sees the load reflected at 1/400 of its actual value.

Example 3

Audio output transformer (tube amp)

Inputs:: Vp=160, Vs=8, Ip=0.1, Zl=8
Output:: n = 20:1; Is = 2 A; Z_primary = 3200 Ω

Output transformer matches a 3.2 kΩ tube plate impedance to an 8 Ω speaker.

When to use this vs other tools

Use this for power and audio transformer sizing. For pulse / flyback / switch-mode transformers the duty-cycle and inductance specs matter more than turns ratio alone.

Ohm's Law
Use after determining secondary V and load Zl to find Is = Vs / Zl directly.
Power (Watts)
Use to verify P_in ≈ P_out for sanity-checking transformer specs.
Audio Impedance
Use when an audio transformer matches a high-impedance source to a low-impedance load (or vice versa).
Voltage Drop
Use to size primary-side conductors based on the higher primary current of step-up arrangements.

Authority note

International Electrotechnical Commission (IEC) & IEEE

IEC 60076 series (power transformers) and IEEE C57 transformer standards

IEC 60076 is the international standard for power-transformer specifications; IEEE C57 is the corresponding US/IEEE standard family. The turns-ratio and impedance-reflection identities used here are textbook Faraday-law derivations that appear identically in both standard families.

Limitations

Ideal-transformer model — real transformers have leakage inductance, winding resistance, and core losses (~1-5% combined).
Assumes AC operation; DC voltages cannot pass through a transformer.
Saturation: applying too much voltage at low frequency drives the core into saturation, collapsing inductance and current-limiting.
Frequency: power transformers are sized for 50/60 Hz; audio output transformers extend to ~20 kHz; SMPS transformers operate ~50-500 kHz with different design rules.

Transformer design for mains-voltage applications requires safety isolation, thermal margin, and certification (UL/CE/CSA). Use ready-made transformers from reputable manufacturers for any installation that connects to the grid.

Frequently asked

Step-up vs step-down?+

n > 1 (Vp > Vs) is step-down (mains to low-voltage). n < 1 is step-up. The current flips: step-down has more secondary current than primary, step-up has less.

Does the same formula work for AC and DC?+

No — transformers only work with AC. The changing magnetic flux is what couples primary to secondary. DC produces a constant flux that does not induce a secondary voltage.

What about losses?+

Real transformers have core loss (hysteresis + eddy) and copper loss (I²R). Efficiency is typically 95-99% for power transformers, 85-95% for small audio transformers.

Why does impedance reflect as n²?+

Voltage divides by n, current multiplies by n. Impedance = V / I, so Z divides by n² when viewed from the secondary or multiplies by n² when viewed from the primary.

Autotransformer?+

A single tapped winding rather than two separate windings. Same Vp/Vs = Np/Ns ratio applies, but autotransformers do not provide galvanic isolation.