Transformer Calculator
Calculate turns ratio, secondary voltage, current and power for ideal transformer circuits.
Component Values
Results
V1/V2 = N1/N2 | I1/I2 = N2/N1
How do transformers work?
A transformer transfers electrical energy between two circuits through electromagnetic induction. The primary winding creates a changing magnetic field in the core, which induces a voltage in the secondary winding. The voltage ratio equals the turns ratio: V1/V2 = N1/N2.
In an ideal transformer, power is conserved: V1 × I1 = V2 × I2. This means a step-down transformer that halves the voltage doubles the current. Real transformers have losses from core hysteresis, eddy currents, and winding resistance, with typical efficiencies of 95–98% for power transformers and 80–90% for small signal transformers.
The turns ratio determines whether the transformer steps voltage up or down. N1/N2 > 1 is step-down (lower secondary voltage), N1/N2 < 1 is step-up (higher secondary voltage). A 1:1 ratio provides galvanic isolation without changing the voltage, useful for safety and noise rejection.
Turns Ratio (N1/N2)
V1 / V2 = N1 / N2Power (VA)
V1 × I1 = V2 × I2Key Points
- Voltage ratio equals turns ratio: V1/V2 = N1/N2
- Current ratio is inverse: I1/I2 = N2/N1
- Ideal power conservation: V1×I1 = V2×I2
- Real efficiency: 80–98% depending on size and type
Applications
- AC mains voltage conversion (step-up/step-down)
- Galvanic isolation for safety
- Impedance matching in audio and RF circuits
- Switch-mode power supply transformers
Practical Examples
Step-down transformer: 230 V primary, 12 V secondary, 1 A secondary load. Find turns ratio and primary current.
N = 12/230 = 0.052 (19.2:1) · I_primary = 1/19.2 = 52 mA
Match a 10 kΩ valve/tube plate impedance to an 8 Ω speaker using an output transformer.
N = √(Z_primary/Z_secondary) = √(10000/8) = 35.4:1 turns ratio
Transformer Equation Reference
Key transformer equations
Turns ratio: a = N1/N2 = V1/V2 = I2/I1
Power: P = V1 × I1 = V2 × I2 (ideal transformer)
Impedance: Z1/Z2 = (N1/N2)²Design Examples
N1/N2 = 230/12 = 19.2 → use 19:1 turns ratio. Secondary current: if P = 24W then I2 = 24/12 = 2A, I1 = 24/230 = 104mA.
Turns ratio = 19:1 · I_secondary = 2 A · I_primary = 104 mA
N1/N2 = 12/120 = 0.1 → use 1:10 turns ratio. Impedance ratio: (1/10)² = 1/100 → 8Ω load appears as 800Ω to primary.
Turns ratio = 1:10 · Reflected impedance = 800 Ω
Design tip
Real transformers have efficiency losses (typically 85–98%).
Always specify VA (volt-amperes), not just watts, for transformer ratings.
Add 20–30% margin to handle inrush current and load variations.Did you know? Michael Faraday demonstrated electromagnetic induction in 1831 using an iron ring with two coils — essentially the first transformer. The modern power grid transformer, which allows high-voltage transmission with low losses, is one of the key inventions enabling electrification.