Electrical Engineering Calculator

Transformer Calculator

Calculate turns ratio, current ratio, primary/secondary currents and apparent power for single-phase and three-phase transformers.

Transformer Configuration

Select system type and which quantity you know

System Type

Known Quantity

Input Parameters

Ideal transformer assumptions

Primary Voltage (V_p)

Rated primary (high or low side) voltage.

Secondary Voltage (V_s)

Rated secondary voltage.

Apparent Power (S)

kVA

Rated apparent power of the transformer.

Engineering Tip

Transformers are rated in kVA, not kW. Always use apparent power when sizing or checking loading, especially with low power-factor loads.

Turns Ratio (a)

27.500

a = V_p / V_s = N_p / N_s

Primary Current

4.55 A

Secondary Current

125.00 A

Apparent Power

50.00 kVA

Current Ratio

0.0364

Governing Formulas (Ideal)

a = V_p / V_s = N_p / N_s

I_p / I_s = 1 / a

S = V × I

a—

Turns / voltage ratio

V_pV

Primary voltage

V_sV

Secondary voltage

I_pA

Primary current

I_sA

Secondary current

SkVA

Apparent power

Assumptions & Notes

Ideal transformer (no losses)
No leakage reactance
No magnetizing current
Balanced three-phase system

Engineering Code

Reuse the transformer calculation in your own engineering workflow.

Python

import math

def transformer(system, Vp, Vs, S_kVA=None, Ip=None, Is=None):
    """
    Ideal transformer calculations.

    system: 'single' or 'three'
    Vp, Vs: primary & secondary voltages (V)
    Provide one of: S_kVA, Ip or Is
    """

    a = Vp / Vs

    if S_kVA is not None:
        S = S_kVA * 1000
        if system == 'three':
            Ip = S / (math.sqrt(3) * Vp)
            Is = S / (math.sqrt(3) * Vs)
        else:
            Ip = S / Vp
            Is = S / Vs
    elif Ip is not None:
        Is = Ip * a
        S = (math.sqrt(3) * Vp * Ip) if system == 'three' else (Vp * Ip)
    elif Is is not None:
        Ip = Is / a
        S = (math.sqrt(3) * Vs * Is) if system == 'three' else (Vs * Is)
    else:
        raise ValueError("Provide S_kVA, Ip or Is")

    return {
        "turns_ratio_a": a,
        "Ip_A": Ip,
        "Is_A": Is,
        "S_kVA": S / 1000
    }


# Example
results = transformer('single', 11000, 400, S_kVA=50)
print(results)

MATLAB

function results = transformer(system, Vp, Vs, S_kVA)
    % Ideal transformer calculations
    % system: 'single' or 'three'

    a = Vp / Vs;
    S = S_kVA * 1000;

    if strcmp(system, 'three')
        Ip = S / (sqrt(3) * Vp);
        Is = S / (sqrt(3) * Vs);
    else
        Ip = S / Vp;
        Is = S / Vs;
    end

    results.a = a;
    results.Ip = Ip;
    results.Is = Is;
    results.S_kVA = S_kVA;
end

% Example
r = transformer('single', 11000, 400, 50);
disp(r);

Excel Formulas

a = Vp/Vs
Ip = S/(Vp)          ' single-phase
Is = S/(Vs)
' three-phase:
Ip = S/(SQRT(3)*Vp)
Is = S/(SQRT(3)*Vs)

Example Calculation

Single-phase transformer: V_p = 11 000 V, V_s = 400 V, rated power S = 50 kVA:

Turns ratio a = V_p / V_s = 27.5

I_p = S / V_p = 4.55 A

I_s = S / V_s = 125 A

Current ratio I_p/I_s = 1/a = 0.0364

Technical Explanation: Transformer Basics

A transformer transfers electrical energy between two or more circuits through electromagnetic induction. Ideal transformers obey simple proportional relationships between primary and secondary voltages, currents and turns.

The turns ratio determines how voltage is stepped up or stepped down, while the current is inversely proportional to the turns ratio (conserving apparent power in the ideal case).

How to Use This Calculator

System Type: Select Single-phase or Three-phase.
Primary & Secondary Voltage: Enter the rated voltages of both sides.
Power or Current: Provide either the rated apparent power (kVA) or one of the currents.
Results: The calculator returns turns ratio, both currents and apparent power.

Key Formulas (Ideal Transformer)

Turns / Voltage ratio: a = V_p / V_s = N_p / N_s
Current ratio: I_p / I_s = 1 / a
Single-phase power: S = V_p × I_p = V_s × I_s
Three-phase power: S = √3 × V_p × I_p = √3 × V_s × I_s

Ideal vs Real Transformer

This calculator assumes an ideal transformer (no losses, no leakage reactance, no magnetizing current). Real transformers have copper losses, iron losses and voltage regulation that must be considered in detailed design.

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Real-World Engineering Cases

Incorrect Transformer Sizing in a Factory Expansion

A new production line was added and the existing 630 kVA transformer became overloaded. The original design had used only active power (kW) instead of apparent power (kVA) and had ignored the low power factor of the motor loads.

Engineering Lesson

Transformers are rated in kVA. Always size them according to the total apparent power demand, including the effect of power factor.

Step-Down Transformer Secondary Overcurrent

A 11 kV / 400 V transformer kept tripping on secondary overcurrent. Calculation showed that the secondary current at full load was significantly higher than the protective device rating because the turns ratio had been misapplied during the design stage.

Engineering Lesson

Always verify both primary and secondary currents from the rated kVA and the actual voltages. The current ratio is the inverse of the voltage ratio.

Frequently Asked Questions

What is the turns ratio of a transformer?

The turns ratio a = N_p/N_s = V_p/V_s. It tells how much the voltage is stepped up or stepped down.

Why is the current inversely proportional to the turns ratio?

In an ideal transformer the apparent power on both sides is equal (S_p = S_s). Therefore if voltage is stepped down, current must be stepped up by the same factor, and vice versa.

Do I use line-to-line or phase voltage for three-phase transformers?

This calculator uses line-to-line voltages together with the √3 factor for three-phase power calculations, which matches the usual nameplate ratings.

What units should I use?

Voltages in volts (V), currents in amperes (A), apparent power in VA or kVA. Turns ratio is dimensionless.

Does this calculator include losses and efficiency?

No. It assumes an ideal transformer. Real transformers have copper and iron losses; efficiency and voltage regulation require additional data (no-load losses, load losses, impedance voltage).