Horsepower Calculator

A horsepower calculator converts torque and engine speed into power with HP = torque × RPM ÷ 5,252. For example, 400 lb-ft of torque at 5,252 RPM is 400 hp to the nearest horsepower, and the same 400 lb-ft at 6,000 RPM makes 457 hp. No dyno sheet? A second mode estimates flywheel horsepower from a quarter-mile elapsed time or trap speed instead, turning a drag-strip time slip into a power figure.

The horsepower formula

Mechanical horsepower from torque and rotational speed is given by:

where torque is in pound-feet (lb-ft) and RPM is engine speed in revolutions per minute. The result is in mechanical (imperial) horsepower. The line is a unit conversion, not an approximation: the only rounding is in the constant itself (5,252.113...), and this calculator uses the full value, so it returns a precise number rather than an estimate.

A worked example

Suppose a V8 puts down 400 lb-ft of torque at 4,400 RPM on the dyno. Plug it in:

So the engine is making about 335 horsepower at that point on its curve. Convert to metric and that is about 249.9 kW (335.1 × 0.7457) or 339.8 PS (335.1 × 1.0139), the same figures the calculator shows for its default inputs. Because peak torque and peak power rarely happen at the same RPM, you would repeat this at several engine speeds to map the full power curve; the highest result is the engine's advertised "peak horsepower."

Torque to horsepower chart (HP at each RPM)

This matrix reads a horsepower straight off HP = torque × RPM ÷ 5,252.11 for common torque and RPM pairs, rounded to whole horsepower. Notice the entire 5,252 RPM column returns HP equal to the torque: the crossover is built into the math.

Why the number 5252?

One horsepower is defined as 33,000 foot-pounds of work per minute (550 per second, the figure James Watt assigned to a working horse). Power equals torque times rotational speed, but rotational speed has to be in radians per minute, so you multiply RPM by 2π. Putting that together:

The 33,000 divided by 2π works out to 5,252.11, which is commonly rounded to 5252. It is a pure unit-conversion constant: it does not depend on the engine, the fuel or anything mechanical.

Why horsepower and torque cross at 5,252 RPM

On a dyno chart that plots horsepower and lb-ft of torque on the same scale, the two curves intersect at about 5,252 RPM. The formula explains it: when RPM equals 5,252.11, the term RPM ÷ 5,252.11 equals 1, so horsepower numerically equals torque. Below that engine speed, torque is the bigger number; above it, horsepower pulls ahead. This is a property of the units, not the engine, so it is true for a diesel pickup and a Formula 1 engine alike.

Horsepower vs. torque: what is the difference?

Torque is the twisting force the crankshaft delivers: how hard it pushes. Horsepower is the rate at which that force does work, so it folds in how fast the engine is spinning. A heavy-duty diesel makes huge torque at low RPM for towing; a motorcycle engine makes modest torque but revs much higher, and the two can reach the same horsepower by very different paths. As a driver, torque is what you feel off the line, while horsepower governs top-end pull and trap speed.

Estimating horsepower from a quarter-mile pass

If you have a drag-strip time slip but no dyno number, switch to the second mode. There are two classic equations. The elapsed-time (ET) equation, commonly attributed to automotive writer Roger Huntington, is:

where weight is the car plus driver in pounds and ET is the quarter-mile time in seconds. A 3,500 lb car running a 13.5-second quarter mile estimates to about 281 hp. The trap-speed equation is:

The same car trapping 102 mph estimates to about 290 hp. Trap speed usually tracks power more reliably than ET because it is less sensitive to launch traction and reaction time: a bad launch wrecks your ET but barely changes how fast you are going at the stripe.

Quarter-mile time to horsepower (3,500 lb car)

Estimated flywheel HP and power-to-weight for a 3,500 lb vehicle (with driver), computed from both equations. Read the ET table from a clean pass; when traction is poor, trust the trap-speed table.

Both tables scale linearly with weight: for a 4,000 lb car, multiply the ET-based HP by 4,000 ÷ 3,500 (about 1.143), so a 13.5-second pass then estimates near 321 hp instead of 281.

How to use this horsepower calculator

Pick the mode that matches the numbers you have:

1. From torque & RPM: enter torque in lb-ft and the engine speed in RPM. Use the quick buttons (3,000 / 5,252 / 6,500 RPM) to jump to common reference points. The result is horsepower, plus kW and PS.
2. From a 1/4-mile pass: enter the vehicle weight including the driver, then choose whether you are estimating from elapsed time or trap speed, and enter that value. The result is an estimated flywheel HP plus a power-to-weight ratio in lb/hp.

The result updates as you type: read the big number at the top, then the table that restates the same power in mechanical, metric, electric and boiler horsepower, kilowatts and watts. Run it again with different inputs to map a power curve (torque mode) or to compare passes (quarter-mile mode). An empty box, a zero or a typo shows a short message instead of a result.

Who this calculator is for

• Enthusiasts and tuners converting a dyno torque-and-RPM reading into a horsepower figure at each point on the curve.
• Drag racers back-calculating engine power from a time slip when no chassis dyno is handy.
• Students and hobbyists learning where the 5,252 constant comes from and why the curves cross.
• Shoppers comparing specs who need to translate between hp, kW and PS across US and metric brochures.
• Anyone with a project build sanity-checking whether a claimed horsepower number is consistent with measured torque.

Converting hp to kW and PS

Several units describe power, and the calculator shows the conversions for you:

• Kilowatts (kW): one mechanical horsepower (550 ft·lbf/s) is 745.69987158227022 W, so multiply hp by 0.7457. So 335 hp = 249.8 kW.
• Metric horsepower (PS / CV): one PS is 735.49875 W, so multiply hp by about 1.01387. So 335 hp = 339.6 PS. PS is slightly smaller than mechanical hp, which is why European brochures show a marginally larger PS figure for the same engine.
• Electric and boiler horsepower: electric horsepower is exactly 746 W (used for motors), and boiler horsepower is about 9,809.5 W (a steam-boiler rating, roughly 13 times larger). Do not mix them up with engine horsepower.
• Back to hp: divide kW by 0.7457, or divide PS by 1.01387.

Quick horsepower-to-kW-and-PS reference:

Power-to-weight ratio

Acceleration depends far more on power-to-weight than on horsepower alone. Divide weight (lb) by horsepower to get pounds per horsepower (lb/hp); lower is quicker. A 3,500 lb car with 350 hp is 10 lb/hp, while the same car at 250 hp is 14 lb/hp. On the 250 hp version, removing 300 lb (to 12.8 lb/hp) helps about as much as adding roughly 23 hp would. The quarter-mile mode reports this ratio so you can see at a glance how "fast" a given build really is.

Flywheel vs. wheel horsepower

There are two horsepower numbers for any car. Flywheel (crank) horsepower is measured at the engine and is what manufacturers advertise. Wheel horsepower (whp) is measured at the drive wheels on a chassis dyno and is lower: the difference is drivetrain loss through the transmission, driveshaft and differential, and it varies with the drivetrain layout and the dyno, so there is no single fixed percentage. The torque formula returns whatever torque you feed it (crank torque in, crank HP out), and the quarter-mile equations are meant to estimate flywheel power, so do not subtract drivetrain loss twice.

What changes the result the most

• RPM: in torque mode, horsepower scales directly with engine speed; the same torque at a higher RPM is more power, which is why high-revving engines make big horsepower from modest torque.
• Weight: in quarter-mile mode, HP scales linearly with weight, so an inaccurate weight (forgetting the driver and fuel) skews the estimate.
• ET and trap speed cubed: both quarter-mile equations raise the time or speed to the third power, so small timing errors get amplified; measure carefully.
• Density altitude: hot, high, humid air costs power at the strip; an uncorrected pass under-reads the engine's sea-level potential.

Tips for an accurate estimate

• Weigh the car with the driver, fuel and everything you raced with: racing weight, not curb weight.
• Use a clean pass: a spun or sandbagged launch ruins ET-based estimates. Prefer the trap-speed equation when traction is questionable.
• For dyno-based math, read torque and RPM at the same instant on the chart, and repeat across the rev range to find peak power.
• Remember the quarter-mile equations assume a roughly typical car shape; very aerodynamic or very draggy vehicles will read off.

Limitations and assumptions

The torque-and-RPM result is mathematically exact for the inputs you give it. The quarter-mile estimates, however, are empirical rules of thumb, not physics-derived guarantees:

• They ignore aerodynamic drag differences, rolling resistance, and tire and gearing effects.
• They are not weather-corrected, so density altitude shifts the answer.
• They estimate flywheel power and assume a reasonably well-executed pass.
• They are meant for cars; motorcycles and unusual vehicles fall outside their assumptions.

For a definitive number, a chassis or engine dynamometer is the right tool. This horsepower calculator is for quick conversions and back-of-envelope checks.

Related calculators

Need a different conversion? A sister tool may fit better:

• For torque from a force and a lever arm, use the Torque Calculator.
• For gear ratios, output speed and torque multiplication, use the Gear Ratio Calculator; for how a tire change affects your speedometer, the Tire Size Calculator.
• For lb-ft to N·m and other units, use the Unit Converter; for mph to km/h, the Miles to km Converter; for vehicle weight in kilograms, the kg to Pounds Converter.
• To measure the gain from a tune, the Percentage Increase Calculator turns before-and-after dyno numbers into a percentage.

About this formula

The core identity HP = torque × RPM ÷ 5,252.11 follows from the definition of horsepower (550 ft·lbf per second, or 33,000 ft·lbf per minute) and the relationship between torque, angular velocity and power. The watt values used for kW, PS, electric and boiler horsepower are the ones listed by NIST. The quarter-mile elapsed-time equation HP = weight / (ET / 5.825)³ and the trap-speed equation HP = weight × (mph / 234)³ are long-established empirical rules of thumb from drag racing, presented here as estimation tools rather than measured values.

Sources

• NIST Special Publication 811, Appendix B.8: Factors for units listed alphabetically (horsepower (550 ft·lbf/s), metric, electric and boiler horsepower in watts; pound-force foot in newton meters).
• NIST: Guide for the Use of the International System of Units (SP 811).