# Torque and Power

> Torque is twisting force; power is how quickly that force does work. Learn how they relate (P = Tω), why gearing changes torque but not power, and how to read an engine's curves.

- Level: Beginner · about 12 minutes · Basics & Fundamentals
- Lesson page: https://autoverse.maxrecursion.dev/topics/torque-and-power

## What you will learn

- Define torque and power and state their units
- Use P = T × ω to convert between torque, engine speed and power
- Explain why a gearbox multiplies torque but cannot add power
- Read a torque and power curve and identify the useful rev range

## The idea, in plain language

Torque is a twisting effort, like the turning force you put on a spanner. Push harder, or use a longer spanner, and the torque goes up. Engines are rated by the torque they put on the crankshaft.

Power is how fast that twisting effort gets work done. A small engine spinning very quickly can make the same power as a large engine turning slowly with more torque. Power is what ultimately decides how fast a car can accelerate at speed and how quickly it can climb a hill.

Gears let the car trade between the two. In first gear the wheels turn slowly but with a lot of torque, which is perfect for pulling away. In top gear the wheels turn quickly with less torque, which is fine once the car is moving.

## The engineering explanation

Torque T is force × lever arm, measured in newton-metres (N·m). Power P is the rate of doing work. For a rotating shaft P = T × ω, where ω is angular speed in radians per second (ω = 2π × rpm / 60). In convenient units, P[kW] = T[N·m] × rpm / 9549. For example, 300 N·m at 4,000 rpm is about 126 kW (roughly 170 PS).

A gear pair with ratio i multiplies torque by i and divides speed by i, so ideal power is unchanged; real gear meshes lose a few per cent as heat. Wheel torque is T_engine × i_gear × i_final × η, and the tractive force at the road is that torque divided by the tyre's rolling radius. Because power is conserved through the gearbox, the maximum tractive force available at any road speed is limited by engine power: F_max ≈ P × η / v.

An engine's torque curve is shaped by how well it breathes: cylinder filling (volumetric efficiency) peaks at the speed where intake and exhaust tuning, valve timing and any boost combine best. Power keeps rising past the torque peak because speed is still increasing faster than torque is falling, until breathing and friction losses cause power to peak and then drop. Drivers get the strongest acceleration in a gear by keeping the engine near its power peak; they get the best efficiency at moderate speed and relatively high load.

## Step by step

1. **Torque is twisting force.** Pushing on the end of a spanner creates a twist around the bolt. Double the push or double the spanner length and the twist doubles. *In engineering terms:* T = F × r. 100 N applied 0.3 m from the axis is 30 N·m. In an engine, cylinder pressure on the piston acts through the crank throw to produce crankshaft torque that varies through the cycle; quoted figures are averages.
2. **Power is torque at speed.** The same torque applied faster gets more work done each second, which is what power measures. *In engineering terms:* P = T × ω with ω = 2π n / 60. 200 N·m at 6,000 rpm (628 rad/s) is about 126 kW — the same as 300 N·m at 4,000 rpm.
3. **Gears trade speed for torque.** A low gear makes the wheels turn slowly but forcefully. A high gear makes them turn quickly but gently. *In engineering terms:* Ratio i: T_out = T_in × i × η, ω_out = ω_in / i. With a 3.5:1 first gear and a 4:1 final drive, 250 N·m at the crank becomes about 3,300 N·m at the wheels after ~94% driveline efficiency.
4. **Read the torque and power curves.** Torque usually rises to a broad peak in the middle of the rev range; power keeps climbing to near the red line. *In engineering terms:* Power peaks above the torque peak because P ∝ T × n. Between the two peaks the engine delivers strong acceleration with a forgiving response; turbocharged engines often show a flat torque plateau from low speed.

## Key concepts

- **Torque**: A twisting force about an axis, measured in newton-metres. (`T = F × r`)
- **Power**: Rate of doing work, measured in watts (kW for engines). (`P = T × ω`)
- **Handy conversion**: Power in kilowatts from torque in N·m and engine speed in rpm. (`P[kW] = T[N·m] × rpm / 9549`)
- **Wheel torque**: Engine torque multiplied by the overall gearing, less driveline losses. (`T_wheel = T_engine × i_gear × i_final × η`)

## Common misconceptions

- **Myth:** Torque makes a car fast; power is just a number. **Reality:** Acceleration at a given road speed depends on wheel torque, which is set by engine power once you are free to choose the best gear. Torque and power describe the same output from different angles.
- **Myth:** A gearbox increases power. **Reality:** Gears multiply torque and divide speed by the same factor. Power stays the same apart from small friction losses.
- **Myth:** Diesels pull harder because they make more power. **Reality:** Diesels often make more torque at low engine speed, but they usually rev lower, so peak power is often similar to or below a comparable petrol engine.

## In the real world

- Changing down a gear to overtake raises engine speed towards the power peak, giving more wheel torque at the same road speed.
- Cycling up a hill: standing on the pedals gives torque; spinning a low gear quickly keeps power up without crushing your knees.
- Two cars with the same peak power but different torque curves can feel very different: a flat torque curve feels strong without many gear changes.

## Common questions

### What is the difference between torque and horsepower?

Torque is a twisting force, measured in newton-metres or pound-feet. Power is the rate at which that force does work, so it depends on how fast the shaft turns: power equals torque multiplied by rotational speed. Horsepower is simply a unit of power.

### Does torque or power decide how fast a car accelerates?

Acceleration depends on the force at the wheels, and gearing can multiply torque but cannot create power. So for cars of the same weight, the one with more power available at that road speed can accelerate harder.

### How do you convert torque to horsepower?

Horsepower equals torque in pound-feet multiplied by rpm, divided by 5,252. In SI units, power in watts equals torque in newton-metres multiplied by angular speed in radians per second, and one kilowatt is about 1.34 horsepower.

## The story behind it

### James Watt (1782–1783)

Gave engines a unit of power by measuring them against horses. Watt had to explain how much work his steam engines could replace, and the customers' benchmark was the horse. In 1782 he found that a brewery horse could do about 32,400 ft·lbf of work per minute, and the next year he and Matthew Boulton standardised the figure at 33,000 ft·lbf per minute. That is the horsepower on every engine spec sheet today.

*Worth knowing:* A popular tale says a brewer demanded an engine matching his strongest horse. The source treats it as legend, and it says where Watt's 180 lbf pull figure came from is unknown.

Sources: [Wikipedia: Horsepower](https://en.wikipedia.org/wiki/Horsepower)

## Related lessons

- [How a Car Works: The Big Picture](https://autoverse.maxrecursion.dev/topics/how-a-car-works)
- [Automatic Transmission](https://autoverse.maxrecursion.dev/topics/automatic-transmission)
- [The Differential](https://autoverse.maxrecursion.dev/topics/differential)
- [Mechanical Sympathy](https://autoverse.maxrecursion.dev/topics/mechanical-sympathy)

## Further reading

- [Torque and BHP explained](https://www.howacarworks.com/technology/torque-and-bhp-explained) — How a Car Works

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Original AutoVerse lesson (AutoVerse original content). Simulation values in AutoVerse labs are illustrative. Source page: https://autoverse.maxrecursion.dev/topics/torque-and-power