Motors and transformers
Transformer voltage and turns ratio
- where
- secondary voltage (V)
- primary voltage (V)
- secondary turns
- primary turns
Explain this equation
Relates the voltages on a transformer's two windings to their numbers of turns. The calculator gives the secondary voltage from the primary voltage and the turns. Use it to check step-down ratios or what a winding should produce.
V_p and V_s are the primary and secondary RMS winding voltages. N_p and N_s are the primary and secondary turns. Fewer secondary turns means a lower secondary voltage.
The same alternating flux links both windings, so every turn has the same voltage induced in it. Each winding's voltage is therefore proportional to its turns, giving V_s = V_p × N_s / N_p.
230 V on 1000 turns with a 100-turn secondary gives 23 V. Double the secondary turns and the output doubles.
Watch out: this is the ideal no-load figure; the real secondary voltage sags a little under load. The same ratio does not mean isolation, since an autotransformer can share it. In three-phase units, star and delta connections make winding and line ratios differ.
In the ideal model, voltage follows the turns ratio. A secondary with fewer turns than the primary gives a lower voltage.
Rearrange before substituting: V_s = V_p × N_s/N_p, or N_s = N_p × V_s/V_p. Keep winding quantities distinct from three-phase line quantities.
Enter your values to see the result.
Common mistake
Do not assume winding voltage ratio always equals three-phase line voltage ratio for unlike connections.
Limits
Ideal transformer approximation with alternating flux; real winding drops and regulation affect loaded voltage. Turns ratio does not establish safe isolation; an autotransformer can have the same ratio without isolation.
Sources
The tools calculate the displayed equation. They do not automatically choose cable sizes, approve installations, supply current regulatory tables, certify equipment or replace inspection and testing.