Transformer Calculator

Calculate turns ratio, secondary voltage, primary and secondary current, and power for electrical transformers. Get step-by-step MathJax formulas for ideal and real transformer analysis.

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About Transformer Calculator

The Transformer Calculator computes turns ratio, secondary voltage, primary and secondary current, power, and impedance transformation ratio for electrical transformers. Enter the primary voltage and number of turns for both windings, with optional current or power values, to get a complete analysis with step-by-step MathJax formulas.

What Is a Transformer?

A transformer is an electromagnetic device that transfers electrical energy between two or more circuits through electromagnetic induction. It consists of a magnetic core with two (or more) coils of wire wound around it. The primary winding receives input power, and the secondary winding delivers output power at a different voltage level.

$$\frac{V_1}{V_2} = \frac{N_1}{N_2} = n$$

where $V_1$ and $V_2$ are primary and secondary voltages, $N_1$ and $N_2$ are the number of turns in each winding, and $n$ is the turns ratio.

Key Transformer Equations

Voltage ratio: The voltage across each winding is proportional to the number of turns:

$$V_2 = V_1 \times \frac{N_2}{N_1}$$

Current ratio: Current is inversely proportional to the turns ratio (for an ideal transformer):

$$\frac{I_1}{I_2} = \frac{N_2}{N_1}$$

Power: For an ideal transformer, power is conserved: $P_{in} = P_{out}$. For real transformers with efficiency $\eta$: $P_{out} = \eta \times P_{in}$.

Step-Down vs. Step-Up Transformers

Step-Down (N₁ > N₂) — reduces voltage, increases current. Common in power distribution (e.g., 120V from 12kV lines) and DC power supplies.
Step-Up (N₁ < N₂) — increases voltage, reduces current. Used in power transmission to reduce line losses and in CRT/high-voltage applications.
Isolation (N₁ = N₂) — provides galvanic isolation without changing voltage. Used in medical equipment, sensitive electronics, and safety applications.

Impedance Transformation

Transformers also transform impedance by the square of the turns ratio:

$$\frac{Z_{primary}}{Z_{secondary}} = \left(\frac{N_1}{N_2}\right)^2 = n^2$$

This property is widely used in audio systems (matching speaker impedance to amplifier output) and RF circuits (antenna impedance matching).

How to Use This Calculator

Enter primary voltage — Input the voltage applied to the primary winding (V₁) and select the unit.
Enter turns — Input the number of turns for the primary winding (N₁) and secondary winding (N₂).
Optional inputs — Provide primary current, power rating, or adjust efficiency to get current and power calculations.
Click Calculate — Press the button to compute all transformer parameters.
Review results — Examine the turns ratio, voltages, currents, power, impedance ratio, transformer diagram, and step-by-step formulas.

Practical Applications

Power distribution — Step-up transformers transmit power at high voltage over long distances, then step-down transformers reduce it for household use.
Electronic power supplies — Mains voltage is stepped down to low voltage (5V, 12V, etc.) for electronic devices.
Audio equipment — Output transformers match vacuum tube or transistor impedance to speakers. Input transformers provide balanced signal isolation.
Welding — Welding transformers step down voltage and step up current to create the high-current arc needed for welding.
Measurement — Current transformers (CTs) and potential transformers (PTs) step down high voltages and currents for safe measurement.

FAQ

What is a transformer turns ratio?

The turns ratio is the ratio of primary winding turns (N₁) to secondary winding turns (N₂). It determines how voltage is transformed: a ratio of 10:1 means the secondary voltage is 1/10 of the primary voltage (step-down), while 1:10 means the secondary is 10 times higher (step-up).

How does a transformer change voltage?

A transformer changes voltage through electromagnetic induction. The alternating current in the primary winding creates a changing magnetic flux in the core, which induces a voltage in the secondary winding. The induced voltage is proportional to the ratio of secondary to primary turns: V₂ = V₁ × (N₂/N₁).

What is the relationship between current and turns ratio?

Current is inversely proportional to the turns ratio. When voltage is stepped down, current is stepped up by the same factor, and vice versa. This conserves power (P = V × I). For an ideal transformer: I₁/I₂ = N₂/N₁.

What is impedance transformation?

A transformer transforms impedance by the square of the turns ratio: Z₁/Z₂ = (N₁/N₂)². This is essential for impedance matching in audio and RF circuits, where maximum power transfer requires the source and load impedances to be matched.

What is transformer efficiency?

Efficiency (η) is the ratio of output power to input power, expressed as a percentage: η = (P_out/P_in) × 100%. Real transformers have losses from core losses (hysteresis, eddy currents) and copper losses (I²R heating in windings). Typical efficiency ranges from 95% to 99% for power transformers.

How many turns should a 12 V secondary have if a transformer has 1,000 primary turns and a 120 V input?

For an ideal transformer, secondary turns equal primary turns multiplied by secondary voltage divided by primary voltage. Here, 1,000 × 12 ÷ 120 gives 100 secondary turns. This is a turns-ratio estimate; a real transformer’s output under load can differ because of winding resistance, core behavior, and losses. Use the specified operating frequency and design limits when building or selecting a transformer.

Can I power a transformer with 12 V DC to get a lower voltage?

A conventional transformer needs changing current, usually AC, to keep inducing voltage in its secondary winding. A steady DC supply produces only a brief change when switched on, then the magnetic field stops changing; it can also cause excessive primary current and heating. Use an appropriate AC source or a designed switching converter for DC-to-DC conversion. Check the transformer’s ratings and intended frequency.

What transformer rating do I need for a 12 V, 2 A load?

The load requires 12 V × 2 A = 24 VA of apparent power. Choose a transformer with a rating at least that high and verify it can supply the required secondary voltage and current under load. Real transformers have losses and voltage regulation, so a little capacity margin may be useful. Check the equipment’s specifications and the transformer’s temperature and duty ratings for the application.

Reference this content, page, or tool as:

"Transformer Calculator" at https://MiniWebtool.com/transformer-calculator/ from MiniWebtool, https://MiniWebtool.com/

by miniwebtool team. Updated: Mar 18, 2026

Developer API available: Run this tool from your app, automation, or agent with one JSON HTTP request. View API docs

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