Torque and Horsepower Converter at RPM

How to Use This Tool

Choose what you want to solve for and fill in the other two. Everything is shown in both imperial and metric because engine figures travel between them constantly.

Where 5252 comes from

Power is the rate of doing work, and rotating work is torque multiplied by angle. So:

power = torque × angular speed

James Watt defined one horsepower as 33,000 foot-pounds of work per minute. One revolution is 2π radians. Put those together and the conversion factor is 33,000 ÷ 2π = 5252.11, which gives the familiar formula:

hp = torque (lb-ft) × rpm ÷ 5252

The metric version uses 60,000 ÷ 2π = 9549.30, so kW = Nm × rpm ÷ 9549. Different number, identical physics.

Why the curves always cross there

Set rpm to 5252 in that formula and it collapses to hp = torque. So on any dyno chart plotted in lb-ft and horsepower, the two lines must meet at 5252 rpm — every engine, every time, with no exceptions.

Verified: 300 lb-ft at 5252 rpm is 300.0 hp. The same 300 lb-ft at 6,000 rpm is 342.7 hp.

It reveals nothing about the engine. It is an artefact of plotting two quantities in units that happen to coincide at that speed. Plot the same engine in Nm and kW and the lines cross somewhere else entirely, because 9549 is a different number. An engine that never reaches 5252 rpm simply has curves that never meet on the chart.

Which is why acceleration follows power, and why a first-gear torque figure means little.

Which number actually matters

A long argument with a short answer: for acceleration, power. For the feel of an engine, torque and where it arrives.

Gearing multiplies torque for free. Put 300 lb-ft through a total ratio of 12:1 and the wheels see 3,600 lb-ft, at one twelfth of the engine speed. What gearing cannot do is create power — it only trades torque against speed, and loses a few per cent to friction.

So quoting torque without a gear ratio says nothing about how quickly something will move. Power is the figure that survives gearing, which is why it predicts acceleration and why heavy machinery with enormous torque figures is still slow.

What torque and its shape do tell you is drivability. An engine making its peak at 1,800 rpm feels effortless and rarely needs a downshift; one making the same peak at 6,500 rpm feels frantic in traffic and identical on a track once the gearbox is used properly.

Which horsepower

Three units are commonly called horsepower and they are not equal:

Mechanical hp — 745.70 W. The usual British and American figure.
PS (metric hp) — 735.50 W, about 1.4% smaller. Common in German and Japanese specifications, and often printed as "hp" in translation.
kW — the actual SI unit and the only unambiguous one.

A 400 PS car is 394.6 hp. That is why the same model appears with two different figures depending on which brochure you read.

Frequently Asked Questions

Why do torque and horsepower cross at 5252 rpm?

Because hp = torque × rpm ÷ 5252, so at exactly 5252 rpm the formula reduces to hp = torque. The number is 33,000 foot-pounds per minute divided by 2π — a unit conversion, not a property of any engine. Plot the same engine in Nm and kW and the lines cross somewhere else.

How do you convert torque to horsepower?

Multiply torque in lb-ft by engine speed in rpm and divide by 5252. In metric, multiply Nm by rpm and divide by 9549 to get kW. Both come from power being torque times angular speed.

Is torque or horsepower more important?

For acceleration, power — because gearing multiplies torque for free but cannot create power. For how an engine feels, torque and where in the rev range it arrives. A torque figure quoted without a gear ratio says nothing about how fast something will go.

What is the difference between hp and PS?

Mechanical horsepower is 745.70 W and PS, the metric version, is 735.50 W — about 1.4% smaller. A 400 PS car is 394.6 hp, which is why the same model shows two different figures in different brochures.

Can gearing increase horsepower?

No. Gearing trades torque against rotational speed, so it multiplies torque at the wheels while power stays the same minus a few per cent of friction. Twelve-to-one gearing turns 300 lb-ft into 3,600 lb-ft at one twelfth the speed, and the power is unchanged.

Do all engines cross at 5252 rpm?

Every engine whose curves are plotted in lb-ft and horsepower and which reaches that speed. Engines that never rev to 5252 have curves that simply never meet on the chart — and nothing is wrong with them.

Torque and Power Cross at 5252 RPM Because of a Unit Conversion

How the calculation works