Transformer Turns Ratio Calculator – Voltage, Current and Impedance
A transformer is two windings sharing one magnetic core, and almost everything you need to know about it falls out of a single chain of equalities: n = N_p / N_s = V_p / V_s = I_s / I_p. This turns ratio calculator works that chain in every direction — give it any complete pair and it derives the rest, including the apparent power on both windings, the reflected impedance, the volts per turn and a realistic primary current once you tell it the efficiency.
What the turns ratio actually tells you
The ratio n is the number of primary turns divided by the number of secondary turns. When n > 1 the transformer is a step-down unit, when n < 1 it is a step-up unit, and when the windings are equal it is an isolation transformer whose whole purpose is the galvanic break rather than any change in voltage. A 1150-turn primary against a 60-turn secondary gives n = 19.167, which turns a 230 V mains supply into 230 / 19.167 = 12 V. Reduced to whole numbers that same winding is 115 : 6, and that pair is what a winder actually counts onto the bobbin.
Why current transforms the other way round
A transformer moves power, it does not create it, so the apparent power S = V × I is the same on both sides of an ideal unit. Dividing the voltage by 19.167 therefore multiplies the current by the same figure, which is why a 5 A load on that 12 V secondary draws only 5 / 19.167 = 0.261 A from the primary — and why the two windings check out at 60 VA each. It is also the reason step-down transformers are wound with thin wire on the many-turn primary and thick wire on the few-turn secondary.
Impedance matching squares the ratio
Impedance is voltage over current, and the transformer scales voltage by n while scaling current by 1/n, so impedance scales by n². The reflected impedance seen looking into the primary is Z_p = n² · Z_s. That single squaring is what makes audio output transformers practical: matching a 5 kΩ valve plate load to an 8 Ω speaker needs a ratio of only √(5000 / 8) = 25 : 1. Run it the other way and the 19.167:1 mains winding above reflects an 8 Ω load as 2938.9 Ω.
V = 4.44 · f · N · B_max · A_c uses the conventional rounded form of 2π/√2 = 4.4429. Every winding table and datasheet quotes 4.44, so this calculator does too — the 0.07 % difference is far smaller than the spread in real core data.
Designing a core from scratch
The volts-per-turn mode runs the EMF equation forwards. At 50 Hz, with 6 cm² of core cross-section worked at a peak flux density of 1.2 T, each turn supports 0.1598 V. A 230 V primary is then 1439 turns and a 12 V secondary 75 turns. Because half a turn cannot be wound, the tool shows the exact requirement, the rounded winding, and the voltage that rounded winding really delivers, alongside a table of the nearby options. Push B_max much above 1.6 T in ordinary grain-oriented silicon steel and the core saturates: the magnetising current spikes, the core overheats, and the winding stops following the turns ratio at all.
From the ideal model to a real transformer
The ideal model assumes perfect coupling, no winding resistance, no leakage inductance and no core loss. Real units lose a few percent, so the efficiency mode takes the output power P_out = V_s · I_s, divides by η to get the input power, and reads the true primary current off that. The same 12 V, 5 A secondary at 95 % efficiency needs 63.16 W in rather than 60 W, pulls 0.275 A from the mains instead of 0.261 A, and dissipates the difference — 3.16 W — as heat in the copper and the core.
Units, checks and where the numbers land
Voltages are accepted in millivolts, volts and kilovolts; currents in microamps through kiloamps; impedances from milliohms to teraohms; core area in mm², cm², in² and more; flux density in tesla, millitesla and gauss. Everything is normalised to SI before the arithmetic and converted back only for display. If you over-specify the problem — supplying both windings and both voltages — and the two ratios disagree by more than half a percent, the tool names both figures instead of quietly preferring one, and it flags a power imbalance whenever the two currents you entered cannot both be true.