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 Principles and Engineering Applications

1. Technical Introduction

Transformers are static electrical machines that transfer energy between circuits using electromagnetic induction. They are essential in power systems for stepping voltage levels up or down, enabling efficient transmission and safe distribution. By conserving apparent power in the ideal case, transformers balance voltage and current across primary and secondary windings. This makes them indispensable in applications ranging from grid-scale substations to small electronic devices.

2. Governing Equations

The fundamental transformer relationships are derived from Faraday’s law of electromagnetic induction:

V_p/V_s = N_p/N_s = a
I_p/I_s = 1/a

Where V_p and V_s are primary and secondary voltages, N_p and N_s are turns, and a is the turns ratio. Apparent power is conserved:

Single-phase: S = V × I
Three-phase: S = √3 × V × I

3. Calculation Method

To determine transformer parameters:

Compute turns ratio from voltage ratings.
Calculate primary current from apparent power and primary voltage.
Calculate secondary current from apparent power and secondary voltage.
Verify current ratio equals inverse of turns ratio.

This ensures consistency and highlights whether protective devices are correctly rated.

4. Input Parameters Explained

Primary Voltage: High-voltage side, often transmission level (e.g., 11 kV).
Secondary Voltage: Low-voltage side, distribution level (e.g., 400 V).
Apparent Power (kVA): Transformer rating, includes both active and reactive power.
System Type: Single-phase or three-phase, affecting power formula.

5. Engineering Interpretation

The turns ratio determines voltage transformation, while current ratio ensures power balance. Engineers interpret these results to size conductors, select protective relays, and verify transformer suitability. For example, stepping down from 11 kV to 400 V increases current dramatically, requiring robust secondary busbars and breakers.

6. Units and Conversion

Standard units are:

Voltage: Volts (V), kilovolts (kV)
Current: Amperes (A)
Power: Volt-amperes (VA), kilovolt-amperes (kVA)
Turns ratio: dimensionless

7. Alternative and General Cases

While the calculator assumes ideal transformers, real-world cases involve:

Autotransformers: Share windings, reducing material but complicating isolation.
Three-winding transformers: Used in industrial plants for multiple voltage levels.
Distribution transformers: Designed for continuous operation with efficiency considerations.

8. Assumptions and Limitations

No copper losses (I²R) or iron losses (hysteresis, eddy currents).
No leakage flux; all flux links both windings.
Perfect voltage regulation assumed.
Neglects magnetizing current and saturation effects.

These assumptions simplify calculations but must be corrected in detailed design using manufacturer data.

9. Practical Engineering Applications

Transformer calculations are applied in:

Power system design: Substation sizing and voltage level selection.
Industrial plants: Matching motor loads to supply voltage.
Renewable integration: Stepping up inverter outputs to grid voltage.
Electronics: Small transformers in chargers and adapters.

10. Safety Factors and Verification

Engineers apply safety margins to account for load fluctuations and harmonics. Verification includes checking nameplate ratings, measuring actual currents, and ensuring protective devices are coordinated. For critical installations, load flow and short-circuit studies confirm transformer adequacy.

In summary, transformer calculations provide essential insight into voltage transformation, current distribution, and power handling. While ideal formulas give quick estimates, real-world design requires accounting for losses, regulation, and efficiency to ensure reliable operation.

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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).