Horsepower from Torque and RPM: How to Calculate

To calculate horsepower from torque and RPM, use the formula: HP = (Torque × RPM) ÷ 5,252. Enter the torque in pound-feet (lb-ft) and the engine speed in revolutions per minute (RPM), and the result is the horsepower at that specific operating point.

Formula

The standard equation for mechanical horsepower is:

HP = (Torque × RPM) ÷ 5,252

Where:

• HP = horsepower (mechanical, 745.7 watts)
• Torque = rotational force in pound-feet (lb-ft)
• RPM = revolutions per minute of the crankshaft or output shaft
• 5,252 = a constant derived from the definition of horsepower (33,000 ft·lb/min ÷ 2Ï€)

If your torque is in newton-meters (N·m), first convert to lb-ft by dividing by 1.35581795, then apply the formula. The constant 5,252 only works with lb-ft and RPM; using N·m directly gives an incorrect result.

Worked Example

Using the calculator defaults: torque = 350 lb-ft, RPM = 5,200.

1. Multiply torque by RPM: 350 × 5,200 = 1,820,000
2. Divide by 5,252: 1,820,000 ÷ 5,252 ≈ 346.5
3. Rounded to two decimals: 346.53 hp

This matches the calculator’s headline output. The second output shows the same torque in N·m: 350 × 1.35581795 ≈ 474.54 N·m. The third output answers a common follow-up: at 350 lb-ft, you need (100 × 5,252) ÷ 350 ≈ 1,501 RPM to produce 100 hp.

Why 5,252? The Origin of the Constant

The number 5,252 comes from James Watt’s definition of horsepower: 33,000 foot-pounds of work per minute. One revolution of a shaft moves a point on the circumference through 2π radians, so the conversion factor is 33,000 ÷ (2π) = 5,252.113…, usually rounded to 5,252. This is why the formula is exact at 5,252 RPM: at that speed, torque in lb-ft numerically equals horsepower. Below 5,252 RPM, torque is higher than horsepower; above it, horsepower is higher.

This is a unit-specific constant. If you measure torque in N·m and power in kilowatts, the constant becomes approximately 9,548.8 (for kW = N·m × RPM ÷ 9,548.8). Always match your units to the constant.

How to Use the Result Correctly

The formula gives instantaneous power at one engine speed, not peak power. An engine’s torque curve varies with RPM, so you must calculate horsepower at multiple points to find the peak. For a dyno graph, each data pair (torque, RPM) yields one horsepower value.

In automotive contexts, “horsepower� usually means brake horsepower (bhp) measured at the crankshaft. Wheel horsepower (whp) is lower due to drivetrain losses (typically 10–20% for front- or rear-wheel drive). The formula works for any rotating shaft—electric motors, pumps, even bicycles—as long as you have the torque and RPM.

If you only know power and RPM, you can rearrange the formula to find torque: Torque = (HP × 5,252) ÷ RPM. This is useful when reading a motor nameplate that lists power and speed but not torque.

Common Mistakes and Unit Mix-Ups

• Using N·m with 5,252: This is the most frequent error. Convert N·m to lb-ft first (divide by 1.35581795) or use the metric constant.
• Confusing peak torque RPM with peak power RPM: They are rarely the same. Peak power always occurs at a higher RPM than peak torque, because power = torque × speed.
• Rounding too early: Rounding torque or RPM before multiplying can shift the result by several horsepower. Keep full precision until the final step.
• Using average torque instead of instantaneous: The formula is point-specific; do not plug in an average torque value across an RPM range.

Also note that the formula assumes a linear relationship at that instant, which is valid for any steady-state rotation. It does not account for friction, heat, or internal losses—those are already reflected in the measured torque value.

Real-World Applications and Limits

This calculation is used in engine tuning, electric motor selection, and even bicycle gear analysis. For an electric motor, torque is often constant up to a base speed, then decreases; the formula helps plot the power curve. For an internal combustion engine, the torque curve is bell-shaped, so horsepower typically peaks near the top of the RPM range.

Limitations: The formula cannot predict torque from horsepower alone unless you also know RPM. It also does not tell you how long an engine can sustain that power—thermal limits, cooling, and component strength matter. For engines with forced induction or variable valve timing, the torque curve may have multiple peaks, so single-point calculations miss the shape.

For rotating equipment like pumps or generators, the same formula applies, but you must ensure the torque and RPM are measured at the same shaft. Gearboxes change torque and RPM inversely, so the product (and thus power) remains constant minus gear losses.

Comparison: Metric vs. Imperial Horsepower

Mechanical horsepower (the one used in the formula) is 745.7 watts. Metric horsepower (PS or CV) is 735.5 watts, about 1.4% lower. If you see a European spec in PS, multiply by 0.98632 to get mechanical hp. The torque constant also changes: for PS with N·m, the constant is 7,122.5 (since 1 PS = 75 kgf·m/s). Most modern dynos report in kW or PS, so be consistent.

For kilowatts, the formula is simply: kW = (N·m × RPM) ÷ 9,548.8. This is the metric equivalent and avoids conversion errors. Many international readers prefer this form.

Frequently Asked Questions

What if my torque is in N·m and RPM is given?

Convert N·m to lb-ft by dividing by 1.35581795, then use the 5,252 formula. Alternatively, compute power in kilowatts directly with kW = (N·m × RPM) ÷ 9,548.8, then convert to hp by multiplying by 1.34102. Both methods give the same result if done correctly.

Why do dyno graphs show horsepower and torque crossing at 5,252 RPM?

Because the formula sets them equal at that speed. If the graph uses lb-ft and hp, the lines will cross at 5,252 RPM. If the graph uses N·m and kW, they cross at 9,548.8 RPM. This is a mathematical artifact, not a physical property.

Can I calculate torque from horsepower and RPM?

Yes, rearrange the formula: Torque (lb-ft) = (HP × 5,252) ÷ RPM. For example, 300 hp at 6,000 RPM gives (300 × 5,252) ÷ 6,000 = 262.6 lb-ft. This is useful when you know a motor’s rated power and speed but need the shaft torque.

Does this formula work for electric motors?

Yes, it applies to any rotating shaft. Electric motors have a constant torque region and a constant power region; the formula accurately calculates power at any point. However, the rated torque on a motor nameplate is usually at the rated speed, not necessarily peak.

What is the difference between brake horsepower and wheel horsepower?

Brake horsepower is measured at the crankshaft, before transmission and drivetrain losses. Wheel horsepower is measured at the tires on a chassis dyno. The difference is typically 10–20% for passenger cars, but varies with drivetrain type. The formula computes the power at the point where torque is measured, so specify which one you have.

Why do some calculators use 5,252 and others use 5,250?

The exact value is 33,000 ÷ (2π) = 5,252.113. Most use 5,252 for simplicity, giving a difference of about 0.02%—negligible for practical purposes. Some older texts round to 5,250, which is slightly less accurate but still within 0.04%.

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in t | Torque | lb-ft | 350 | 0 | 100000
in r | Engine speed | RPM | 5200 | 0 | 20000
out hp | Horsepower | hp | (t * r) / 5252 | 2
out trq | Torque in N·m | N·m | t * 1.35581795 | 2
out rpm2 | RPM for 100 hp at this torque | RPM | (100 * 5252) / t | 0