What formula is used to derive current from ohms?

Ohm's law: I = V / R. Once current is known, power is calculated as P = V × I = V² / R for DC circuits. The calculator uses this derived current in the horsepower formulas.

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 / R × PF × Eff) / 746. The power factor accounts for the phase difference between voltage and current in AC circuits.

What is the three-phase AC formula?

HP = (3 × V² / R × PF × Eff) / 746. For a balanced three-phase load with per-phase resistance R and line-to-neutral voltage V, total three-phase power is three times the single-phase 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

Name: Ohms to Horsepower Calculator
Availability: InStock
Author: Nham Vu

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

Circuit Parameters

Circuit Type

Resistance (Ω)

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 / R × PF × Eff) / 746

Three-Phase AC

HP = (3 × V² / R × PF × Eff) / 746

Ohm’s law: I = V / R • 1 HP = 746 W • Eff = efficiency fraction

Result copied!

Summary

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

How it works

Select your circuit type: DC, single-phase AC, or three-phase AC.
Enter the resistance in ohms (Ω) — this is the total load or winding resistance.
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), computes input power, applies efficiency, then converts watts to horsepower using 1 HP = 746 W.

Use cases

Estimate the horsepower output of a motor when only its winding resistance and supply voltage are known.
Verify that a resistance-limited circuit can deliver enough power for a mechanical load.
Cross-check motor nameplate ratings against measured resistance values.
Design motor control circuits by working backward from required HP to allowable resistance.
Size protective fuses and breakers based on derived current and power.
Evaluate heating element power output in resistive load applications.
Troubleshoot under-performing motors by comparing theoretical HP to measured shaft output.
Convert resistance data from motor datasheet to horsepower for quick load assessments.

Frequently Asked Questions

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