03 // Bidirectional STEM Calculators // ENGINEERINGV_s = V_p × (N_s / N_p)

Transformer Voltage & Turns Ratio Calculator

Faraday's Law of Electromagnetic Induction dictates that in an ideal magnetic-core transformer, the ratio of secondary to primary RMS voltage equals the ratio of secondary to primary winding turns: V_s = V_p × (N_s / N_p).

V_s = V_p × (N_s / N_p)

Pick which value you want to calculate (or type into any field):Solving for: V_s — Secondary Output Voltage

Secondary Output VoltageCalculated

RMS AC voltage across secondary winding

0.1500,000.00

Primary Input Voltage

RMS AC voltage applied to primary winding

0.1500,000.00

Primary Winding Turns

Number of wire turns on primary coil

1100,000.00

unit

Secondary Winding Turns

Number of wire turns on secondary coil

1100,000.00

unit

Calculated Result · Secondary Output Voltage (V_s)

24V

Converted units:

Step-by-Step Calculation

01Canonical Law: V_s = V_p × (N_s / N_p)

02Given Inputs (Base Units): V_p = 240 V, N_p = 500, N_s = 50

03Solve for V_s (Secondary Output Voltage): V_s = 24 V

Real-World Reference Values

Step-Down Control Transformer240V → 24V (10:1 Turns Ratio)

HVAC & industrial PLC contactor rail

Current Transformation RuleI_s / I_p = N_p / N_s

Stepping voltage down 10× steps available current up 10×

Reflected Impedance RatioZ_p = Z_s × (N_p / N_s)²

Impedance transforms with the square of the turns ratio

20-Row Comparison Table

Secondary Output Voltage (V_s) · Primary Input Voltage (V_p)

Compare across:

Transformer Voltage & Turns Ratio Calculator — Primary Input Voltage → Secondary Output Voltage
#	Primary Input Voltage (V)	Secondary Output Voltage (V)	Δ %
01	240 VCurrent	24 V	0.00%
02	3,631.15 V	363.1147 V	+1412.98%
03	7,262.19 V	726.2193 V	+2925.91%
04	10,893.24 V	1,089.32 V	+4438.85%
05	14,524.29 V	1,452.43 V	+5951.79%
06	18,155.33 V	1,815.53 V	+7464.72%
07	21,786.38 V	2,178.64 V	+8977.66%
08	25,417.43 V	2,541.74 V	+10490.59%
09	29,048.47 V	2,904.85 V	+12003.53%
10	32,679.52 V	3,267.95 V	+13516.47%
11	36,310.57 V	3,631.06 V	+15029.40%
12	39,941.61 V	3,994.16 V	+16542.34%
13	43,572.66 V	4,357.27 V	+18055.27%
14	47,203.71 V	4,720.37 V	+19568.21%
15	50,834.75 V	5,083.48 V	+21081.15%
16	54,465.80 V	5,446.58 V	+22594.08%
17	58,096.85 V	5,809.68 V	+24107.02%
18	61,727.89 V	6,172.79 V	+25619.96%
19	65,358.94 V	6,535.89 V	+27132.89%
20	68,989.99 V	6,899.00 V	+28645.83%

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Frequently Asked Questions

Why does a transformer only work with AC or pulsed DC?+

Faraday's law requires a time-varying magnetic flux (dΦ/dt) to induce voltage; steady DC produces zero flux change and saturates the core.

How do I calculate secondary current from primary current?+

In an ideal transformer, apparent power is conserved (V_p × I_p = V_s × I_s), so current scales inversely with turns: I_s = I_p × (N_p / N_s).

How is impedance matched using a transformer?+

Reflected primary impedance equals Z_p = Z_s × (N_p / N_s)², so a 2:1 turns ratio matches a 32 Ω source to an 8 Ω load.