Ideal Transformer Calculator
Enter any combination of primary voltage, secondary voltage, primary turns, and secondary turns to solve for the remaining transformer parameters instantly. Choose what you want to solve for - secondary voltage, primary voltage, secondary current, primary current, turns ratio, or reflected impedance - and the calculator fills in the result with a full step-by-step breakdown. Covers both step-up and step-down configurations for AC power and audio transformer design.
Formula
Worked example
A step-down transformer has N1 = 1000 turns and N2 = 100 turns. The primary voltage is 240 V. Turns ratio: a = 1000/100 = 10. Secondary voltage: V2 = 240/10 = 24 V. If the secondary load is 10 ohm, secondary current I2 = 24/10 = 2.4 A, primary current I1 = 2.4/10 = 0.24 A, and reflected impedance Z1 = 10^2 x 10 = 1000 ohm. Power check: 240 V x 0.24 A = 24 V x 2.4 A = 57.6 VA.
What is an ideal transformer?
An ideal transformer is a theoretical two-winding device that transfers electrical energy between circuits with 100% efficiency and no losses. It consists of a primary winding with N1 turns and a secondary winding with N2 turns wound on a common, lossless magnetic core. Real transformers are designed to get as close as possible to this ideal, with modern power transformers reaching 98-99.5% efficiency. The ideal transformer model is used in circuit analysis and engineering design because it captures the essential electromagnetic relationships without the complexity of leakage inductance, winding resistance, or core losses. It obeys three fundamental laws: the voltage ratio equals the turns ratio, the ampere-turns (current times turns) are conserved across both windings, and power in equals power out.
The four key transformer formulas
The turns ratio a = N1/N2 governs all transformer behaviour. Voltage scales in direct proportion to turns: V2 = V1 x (N2/N1) = V1/a, so a step-down transformer (N1 > N2) reduces voltage and a step-up transformer (N1 < N2) raises it. Current scales in inverse proportion: I2 = I1 x (N1/N2) = I1 x a, keeping power (P = V x I) conserved on both sides. Impedances reflect across the transformer as the square of the turns ratio: Z1 = a^2 x Z2, which is exploited in audio engineering and RF matching circuits to maximise power transfer. For example, a 4-ohm speaker can appear as 400 ohm at the amplifier output when a 10:1 step-down transformer sits between them, matching the amplifier output impedance and improving power delivery.
Step-up vs step-down vs isolation transformers
A step-down transformer (N1 > N2, a > 1) reduces voltage and increases current proportionally - used in wall adapters, distribution substations, and appliance power supplies. A step-up transformer (N1 < N2, a < 1) raises voltage and reduces current - used in power plant generators to boost voltage to transmission levels (often 110 kV to 765 kV) to minimise resistive losses over long distances. An isolation transformer (N1 = N2, a = 1) passes the same voltage and current but breaks the direct electrical connection between primary and secondary circuits, providing safety, reducing common-mode noise, and blocking DC. The calculator handles all three configurations automatically once you enter the primary and secondary turns.
How to use this calculator and interpret the results
Select the quantity you want to solve for from the dropdown, then fill in the known values. For secondary voltage: enter V1, N1, and N2. For reflected impedance: enter V1, N1, N2, and the secondary load impedance Z2 - the result is how that load appears from the primary side, which tells you the current draw and allows impedance matching. The step-by-step panel shows the exact arithmetic so you can verify your own hand calculations or present the work in a report. The chart shows how the secondary voltage would change across a range of turns ratios for your primary voltage, useful when iterating a winding design.
Common transformer configurations
| Configuration | Turns ratio (N1:N2) | Voltage change | Typical use |
|---|---|---|---|
| Mains to 12 V | 20:1 | 240 V - 12 V | Low-voltage DC power supplies |
| Mains to 24 V | 10:1 | 240 V - 24 V | HVAC controls, doorbells |
| Isolation (1:1) | 1:1 | No change | Safety isolation, noise reduction |
| Audio step-up | 1:3 | 10 V - 30 V | Microphone preamplifiers |
| Grid step-up | 1:100 | 11 kV - 1.1 MV | High-voltage transmission |
| Distribution step-down | 5:1 | 11 kV - 2.2 kV | Local power distribution |
Typical turns ratios and their applications. An ideal transformer with turns ratio a steps voltage by 1/a and current by a.
Frequently asked questions
What is the turns ratio of a transformer?
The turns ratio (a) is the number of primary winding turns (N1) divided by the number of secondary turns (N2): a = N1/N2. It determines how voltage and current are scaled between windings. A ratio of 10:1 means the secondary voltage is one-tenth the primary, and the secondary current is ten times the primary current.
Why does an ideal transformer conserve power?
In an ideal transformer there are no losses: no winding resistance, no core hysteresis losses, and no eddy-current losses. Because energy cannot be created or destroyed, all the power entering the primary (V1 x I1) must leave through the secondary (V2 x I2). Voltage and current scale in opposite directions by the same factor (the turns ratio), so their product stays constant.
What is reflected impedance and why does it matter?
Reflected impedance is the secondary load impedance as it appears to the primary circuit after transformation. The formula is Z1 = a^2 x Z2, where a is the turns ratio. A 10:1 transformer reflects a 10-ohm secondary load as 1000 ohm on the primary. This matters in audio amplifiers and RF circuits, where transformers are used to match a high-impedance source to a low-impedance load (or vice versa) to achieve maximum power transfer.
How is an ideal transformer different from a real transformer?
An ideal transformer assumes zero winding resistance, zero leakage flux, zero core losses (hysteresis and eddy currents), infinite core permeability, and 100% magnetic coupling between windings. Real transformers have copper losses in the windings, iron losses in the core, leakage inductance that limits high-frequency performance, and an efficiency below 100% (typically 95-99.5% for power transformers). For most engineering calculations up to medium frequencies, the ideal model is a good first approximation.
Can I use this calculator for three-phase transformers?
This calculator models a single-phase ideal transformer. For a three-phase transformer, the same per-phase equations apply once you account for the winding connection (delta or wye). In a wye-delta configuration, the line-to-line voltage ratio differs from the turns ratio by a factor of the square root of 3 (approximately 1.732). Per-phase analysis using this calculator is a valid starting point before adding the three-phase correction factors.
What happens if the turns ratio is exactly 1:1?
A 1:1 turns ratio gives a = 1, so the secondary voltage equals the primary voltage and the secondary current equals the primary current. No voltage or current transformation occurs, but the primary and secondary circuits are still electrically isolated from each other. This is the basis of isolation transformers, which are used for safety (breaking the connection to earth on medical equipment, for example) and for reducing common-mode electrical noise.