What formula is used to derive current from ohms?

Ohm's law: I = V / R for DC circuits or I = V / Z for AC circuits where Z is load impedance. Once current is known, real power is calculated as P = V × I = V² / R for DC circuits.

What is the DC circuit formula?

HP = (V² / R × Eff) / 746. Voltage squared divided by resistance gives input power in watts; multiplied by efficiency gives mechanical output; divided by 746 converts to horsepower.

What is the single-phase AC formula?

HP = (V² / Z × PF × Eff) / 746, where Z is the load impedance in ohms, V is line-to-neutral voltage, PF is power factor, and Eff is efficiency. The current is I = V / Z and apparent power is S = V × I.

What is the three-phase AC formula?

HP = (3 × V² / Z × PF × Eff) / 746. For a balanced three-phase load with per-phase impedance Z and line-to-neutral voltage V, total apparent power is 3 × V × I and real power is scaled by the power factor.

Can I calculate motor horsepower from winding resistance?

No. Never calculate motor running horsepower or size circuit protection from cold DC winding resistance. Running motors generate back-electromotive force (back-EMF) that limits running current. Dividing supply voltage by cold winding resistance gives locked-rotor or fault current, which is vastly higher than normal running power.

Why does resistance need a voltage input?

Resistance alone does not define power — you need voltage (or current) to calculate it. Using V and R together gives current via Ohm's law, from which power and finally horsepower are determined.

What motor efficiency should I use?

Standard induction motors typically run at 85–95% efficiency. High-efficiency (IE3/IE4) motors can reach 96–97%. If the efficiency is unknown, 90% is a reasonable default for general estimation.

Why is 746 used to convert watts to horsepower?

One mechanical horsepower equals 745.69999… watts, conventionally rounded to 746 W. This definition traces back to James Watt's 18th-century comparisons with draft horse output.

Ohms to Horsepower Calculator

Convert resistance or impedance (ohms) and voltage to horsepower for DC, single-phase AC, or three-phase AC circuits.

Circuit Parameters

Circuit Type

Resistance / Impedance (Ω) (R for DC, Z for AC)

Voltage (V)

Motor Efficiency (%) (1 – 100)

Result

Enter values and press Calculate

Formula Reference

DC Circuits

HP = (V² / R × Eff) / 746

Single-Phase AC

HP = (V² / Z × PF × Eff) / 746

Three-Phase AC

HP = (3 × V² / Z × PF × Eff) / 746

Ohm’s law: I = V / R (DC) or V / Z (AC) • 1 HP = 746 W • Note: Running motors generate back-EMF; do not use cold winding resistance for running horsepower.

Result copied!

Summary

This calculator converts electrical resistance or AC impedance measured in ohms (Ω) and supply voltage (V) into equivalent mechanical power in horsepower (HP). Using Ohm's law and circuit power formulas, the tool derives circuit current and input wattage for DC, single-phase AC, or balanced three-phase AC loads, applying efficiency and power factor. Note: In motor circuits, running current is limited by back-EMF and inductive impedance; never use static motor winding DC resistance to calculate running horsepower or size circuit protection.

How it works

Select your circuit type: DC, single-phase AC, or three-phase AC.
Enter the load resistance (R) for DC or equivalent load impedance (Z) for AC in ohms (Ω).
Enter the supply voltage in volts (V).
Enter the motor efficiency as a percentage (typically 85–95%).
For AC circuits, enter the power factor (0 – 1).
Click Calculate. The tool derives current via Ohm's law (I = V / R or I = V / Z), computes real input power, applies efficiency, then converts watts to horsepower using 1 HP = 746 W.

Use cases

Calculate the mechanical horsepower equivalent of electrical heating elements and resistive banks.
Determine shaft horsepower equivalent delivered by a DC circuit with known running load resistance.
Evaluate AC load circuits using equivalent operating impedance (Z) and power factor.
Convert generator load-bank resistance and voltage measurements to mechanical brake horsepower requirements.
Verify power dissipation and horsepower requirements for dynamic braking resistors.
Model electrical-to-mechanical conversion efficiency across DC, single-phase, and three-phase systems.

Frequently Asked Questions

Last updated: 2026-05-23 · Reviewed by Nham Vu