Circuit Breaker Sizing with Safety Margin

Inputs

Enter the load power, supply voltage and power factor (cos θ). For a three-phase supply, V is the line-to-line voltage and the current is divided by √3. Advanced mode lets you change the safety margin.

Results

Power triangle

Real power P does the work; reactive power Q is exchanged with the supply; apparent power S = P / cos θ is what the wiring and the breaker actually carry. A lower power factor means a larger S, so a higher current for the same useful power.

Breaker current vs load power

Required breaker current rises linearly with load power at fixed voltage. The solid teal line uses your power factor; dashed lines show other power factors. The amber dot is your operating point and the horizontal dashed line is the selected standard rating.

Breaker size vs load size

Press Calculate to fill this table.

Each row is the largest load that breaker can carry with your safety margin: P_max = k · V · cos θ · I_rating / (1 + margin). The highlighted row is the breaker recommended for your load. It uses the supply type, voltage, power factor, margin and series chosen above.

Common examples

Computed by the same engine. Illustrative values only, not a substitute for a design to your local wiring rules.

Formula

• P: real power of the load, in watts
• V: supply voltage, in volts (line-to-line for three-phase)
• cos θ: power factor of the load, between 0 and 1
• 1.25: the 25% safety margin, applied to the calculated load current

Single-phase: I = P / (V · cos θ). Three-phase: I = P / (√3 · V · cos θ). The breaker design current is then I × (1 + margin), and the breaker chosen is the smallest standard rating that is at least that value.

Example — a 5 kW single-phase load at 230 V and cos θ = 0.9. I = 5000 / (230 × 0.9) = 24.16 A. With the 25% margin, I_breaker = 24.16 × 1.25 = 30.19 A. The next standard IEC rating is 32 A.

Example — a 10 kW three-phase load at 400 V and cos θ = 0.85. I = 10 000 / (√3 × 400 × 0.85) = 16.98 A. With the margin, 21.2 A, so the next standard rating is 25 A.

The 25% margin follows the common practice of sizing overcurrent protection at 125% of a continuous load. It is a sizing convention, not a guarantee of protection. The breaker must also protect the conductor, so the cable's current-carrying capacity (after derating for temperature, grouping and installation method) must be at least the breaker rating. Motors and other loads with high starting current may need a breaker with a suitable trip curve. Always follow your local wiring regulations and have the design checked by a qualified electrician.

Advanced mode adds the editable margin, the next lower standard rating, the design current at unity power factor, and the working steps.

Key relations

References

• Wikipedia, Circuit breaker
• Wikipedia, Power factor
• Wikipedia, Three-phase electric power
• NFPA 70 (National Electrical Code): continuous-load and standard-rating rules
• IEC: IEC 60898-1 and IEC 60947-2 for breaker standards

How to Use This Tool

1. Choose single-phase or three-phase and the standard series (IEC or NEC/UL).
2. Enter the load power, voltage and power factor, or pick a preset.
3. In Advanced, change the safety margin if your rules require a different value.
4. Click Calculate and read the breaker current and the recommended standard rating.
5. Check the power triangle and the chart, then verify cable size and local rules.

What This Tool Offers

• I_breaker = (P / (V · cos θ)) × 1.25 for single-phase and three-phase loads
• Next standard rating from the IEC or NEC/UL series
• Apparent and reactive power, power factor angle, and breaker utilisation
• Maximum load the selected breaker supports at your margin
• Power triangle diagram and current-vs-power chart

Disclaimer. This tool is for estimation and education. It does not account for cable ampacity, derating, motor starting current, short-circuit rating, discrimination or local regulations. Electrical work should be designed and verified by a qualified person.