Transformer Turns Ratio Calculator

How a Transformer Works A transformer operates on the principle of electromagnetic induction, discovered by Michael Faraday in 1831 in England. Alternating current flowing through the primary coil creates a constantly changing magnetic field in the iron core, and that changing field induces a voltage in the secondary coil.
Only AC does this. Direct current creates a static magnetic field, which induces nothing at all.

The Turns Ratio Law The ratio of primary to secondary voltage exactly equals the ratio of turns: V1/V2 = N1/N2. This is precise for an ideal transformer. Real transformers are 95 to 99% efficient, with losses from resistance in the copper windings (copper loss) and from eddy currents and hysteresis in the iron core (iron loss). High-frequency switching power supplies use ferrite cores instead of iron to reduce these losses.

Current Goes the Other Way While voltage steps up with more secondary turns, current steps down by the same ratio. This is required by conservation of energy: power in equals power out. Double the voltage and you halve the current.

Be careful which way round the ratio is written, because both orders are in common use and they mean opposite things. This page states it as N₁:N₂, primary first, which is the convention the calculator above uses. So 10:1 is a step-down transformer with ten times more turns on the primary, and a step-up is 1:10. Get that backwards and you have specified a transformer that does the reverse of what you wanted. This is why power is transmitted at high voltage: fewer amps for the same watts means far less heat lost in the line, since those losses go as the square of the current.

The Power Grid’s Remarkable Efficiency In the US, power plants generate electricity at 15,000 to 25,000V. Transmission substations step it up to somewhere between 115,000 and 765,000V for long-distance lines. Distribution substations bring it back down to 4,000 to 35,000V for neighborhoods, and a pole or pad transformer takes the last step to 120/240V for your home.
The whole multi-stage system loses only about 5 to 8% of the power it carries, which took decades of engineering to reach.

Impedance Transformation Here is the property most people miss: a transformer transforms impedance by the SQUARE of the turns ratio, so a 10:1 winding gives a 100:1 impedance change. That is what makes it indispensable in audio. A vacuum tube output stage wants to see something around 5,000 ohms, and a speaker is 8 ohms; an output transformer with the right ratio bridges the two so power actually transfers instead of bouncing back. It is also why vintage hi-fi gear carries those heavy output transformers, and why cheap ones ruin the sound.