# Units of Torque

Last Updated: April 25, 2024

## Units of Torque

Torque is a fundamental concept in physics and engineering, describing the rotational force applied to an object. It is a measure of how much a force acting on an object causes that object to rotate. The point where the force is applied is crucial in determining the amount of torque.

### What are Units of Torque?

Units of torque play a critical role in various fields such as mechanical engineering, physics, and automotive design. They are fundamental in quantifying the rotational force applied to objects.

### SI Unit of Torque

newton meter (N·m)

The newton meter (N·m) stands as the official SI unit for measuring torque. It quantifies the rotational force when a force of one newton is applied perpendicularly to a moment arm that extends one meter from the rotation axis.

### CGS Unit of Torque

dyne-centimeter (dyn·cm)

In the Centimeter GramSecond(CGS) system, the unit of torque is known as the dyne-centimeter (dyn·cm). This unit measures the torque resulting from a force of one dyne applied perpendicularly to a lever arm one centimeter long.

## Formula of Torque

The formula for torque (τ) can be expressed simply as:

𝜏=𝑟×𝐹
• 𝜏 is the torque,
• 𝑟 is the length of the lever arm (radius),
• 𝐹 is the force applied perpendicular to the lever arm.

### Newton Meter (N·m)

1 N·m = 1 N × 1 m

The Newton Meter is the SI unit of torque, named for Sir Isaac Newton. It measures the torque resulting from a force of one newton applied perpendicularly to a point one meter from the pivot point. It is universally used in science and engineering to specify rotational force.

### Pound-foot (lb-ft)

1 lb-ft = 1 lb × 1 ft

This unit is widely used in the United States, particularly in automotive and mechanical engineering. It represents the torque produced by one pound-force acting at a radius of one foot from the center of rotation.

### Dyne-centimeter (dyn·cm)

1 dyn·cm = 1 dyn × 1 cm

A dyne-centimeter is the CGS unit of torque. It measures the torque resulting from a force of one dyne applied at a radius of one centimeter from the rotation axis, often used in physics to describe small-scale rotational forces.

### Kilogram-meter (kg·m)

1 kg·m = 1 kg × 9.8 m/s² × 1 m

This unit measures torque using the metric system, where one kilogram-force meter is the torque produced by one kilogram-force acting at a lever arm one meter long.

### Pound-inch (lb-in)

1 lb-in = 1 lb × 1 in

The pound-inch is another imperial unit of torque, commonly used in various applications requiring finer measurements than pound-feet, such as in small machinery or aviation.

## Conversion of Torque Units

Here’s a table format for different units of torque, showing conversion factors between common units like Newton Meters, Pound-feet, Dyne-centimeters, and Kilogram-meters:

### Newton Meter to Pound-foot

• Conversion: 1 lb-ft = 1.35582 N·m
• Example: To convert 100 Newton Meters to Pound-feet:
• 100 N·m / 1.35582 = 73.76 lb-ft

### Newton Meter to Dyne-centimeter

• Conversion: 1 N·m = 1.0E+7 dyn·cm
• Example: To convert 50 Newton Meters to Dyne-centimeters:
• 50 N·m × 1.0E+7 = 5.0E+8 dyn·cm

### Newton Meter to Kilogram-meter

• Conversion: 1 N·m = 0.10197 kg·m
• Example: To convert 30 Newton Meters to Kilogram-meters:
• 30 N·m × 0.10197 = 3.0591 kg·m

### Pound-foot to Newton Meter

• Conversion: 1 lb-ft = 1.35582 N·m
• Example: To convert 45 Pound-feet to Newton Meters:
• 45 lb-ft × 1.35582 = 61.012 N·m

### Pound-foot to Dyne-centimeter

• Conversion: 1 lb-ft = 1.38255E+7 dyn·cm
• Example: To convert 20 Pound-feet to Dyne-centimeters:
• 20 lb-ft × 1.38255E+7 = 2.7651E+8 dyn·cm

### Pound-foot to Kilogram-meter

• Conversion: 1 lb-ft = 0.138255 kg·m
• Example: To convert 15 Pound-feet to Kilogram-meters:
• 15 lb-ft × 0.138255 = 2.073825 kg·m

### Dyne-centimeter to Newton Meter

• Conversion: 1 dyn·cm = 1.0E-7 N·m
• Example: To convert 5.0E+8 Dyne-centimeters to Newton Meters:
• 5.0E+8 dyn·cm × 1.0E-7 = 50 N·m

### Dyne-centimeter to Pound-foot

• Conversion: 1 dyn·cm = 7.37562E-8 lb-ft
• Example: To convert 2.0E+8 Dyne-centimeters to Pound-feet:
• 2.0E+8 dyn·cm × 7.37562E-8 = 14.75124 lb-ft

### Dyne-centimeter to Kilogram-meter

• Conversion: 1 dyn·cm = 1.01972E-6 kg·m
• Example: To convert 1.0E+9 Dyne-centimeters to Kilogram-meters:
• 1.0E+9 dyn·cm × 1.01972E-6 = 1019.72 kg·m

### Kilogram-meter to Newton Meter

• Conversion: 1 kg·m = 9.80665 N·m
• Example: To convert 3 Kilogram-meters to Newton Meters:
• 3 kg·m × 9.80665 = 29.42 N·m

### Kilogram-meter to Pound-foot

• Conversion: 1 kg·m = 7.23301 lb-ft
• Example: To convert 5 Kilogram-meters to Pound-feet:
• 5 kg·m × 7.23301 = 36.16505 lb-ft

### Kilogram-meter to Dyne-centimeter

• Conversion: 1 kg·m = 9.80665E+7 dyn·cm
• Example: To convert 2 Kilogram-meters to Dyne-centimeters:
• 2 kg·m × 9.80665E+7 = 1.96133E+8 dyn·cm

## What is the measurement of torque?

Torque measures the rotational force applied around a pivot point, calculated as the product of force and the perpendicular distance from the pivot.

## What is torque measured in US units called?

In US units, torque is commonly measured in pound-feet (lb-ft).

## Does horsepower equal torque?

Horsepower does not equal torque; rather, horsepower quantifies the rate at which work is done, incorporating both torque and rotational speed in its calculation.

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