Introduction
Torque is the turning force that makes things rotate around a point. When you use a wrench to tighten a bolt or push a door open, you are applying torque. The basic formula is simple: torque equals force times distance times the sine of the angle (τ = r × F × sin θ). A bigger force or a longer lever arm creates more torque, which is why a long wrench loosens a stuck bolt more easily than a short one.
This torque calculator lets you solve for torque, force, or lever arm distance across six different modes. Use the Basic Torque tab for straightforward problems involving a single force on a lever arm. Switch to Rotational Power to find the relationship between torque, speed, and power in motors or engines. The Leadscrew Drive, Belt & Pulley, and Rack & Pinion tabs handle common mechanical systems, while the Multiple Forces tab adds up torques from several forces acting at once. Every result is shown in both metric (N·m) and imperial (lb·ft) units, and a live vector diagram helps you see how force, distance, and angle work together. Quick presets for real-world setups like a bicycle pedal or lug nut let you get started in one click.
How to use our Torque Calculator
Enter your known values such as force, distance, and angle, and this calculator will compute the resulting torque, power, or related mechanical output across six different modes.
Calculation Mode: Choose from six tabs at the top — Basic Torque, Rotational Power, Leadscrew Drive, Belt & Pulley, Rack & Pinion, or Multiple Forces — depending on the type of torque problem you need to solve.
Quick Presets: Click a preset button like Wrench, Door Handle, Bicycle Pedal, Lug Nut, or Engine Torque to auto-fill common real-world values and save time.
Solve For (Basic Torque): Pick whether you want to solve for torque, force, or distance. The calculator will find the unknown value using the other two inputs you provide. If you need to determine the force required for a specific torque, this mode makes it easy.
Force: Enter the amount of force being applied and select its unit from the dropdown — Newtons (N), pounds-force (lbf), kilogram-force (kgf), dynes, or ounces. Our dedicated force calculator can help you determine the force from mass and acceleration if needed.
Distance / Lever Arm: Enter the length from the pivot point to where the force is applied. Choose your unit — meters, feet, centimeters, inches, or millimeters. You can use our distance calculator if you need to compute the lever arm from coordinate points.
Angle: Enter the angle between the force and the lever arm in degrees, or drag the slider. An angle of 90° gives the maximum torque.
System Efficiency: Enter the efficiency of your system as a percentage. Use 100% for an ideal system with no energy loss, or a lower value to account for friction.
Safety Factor: Enter a safety factor to multiply the torque result. A value of 1 means no extra safety margin; higher values add a buffer for real-world use.
Direction: Select whether the torque acts in a clockwise or counterclockwise direction.
Rotational Power Tab: Enter any two of torque, rotational speed (in RPM, rad/s, or Hz), and power (in kW, HP, or W), then choose which value you want to solve for. For automotive applications, our horsepower calculator provides additional power conversion tools.
Leadscrew Drive Tab: Enter the lead of the screw in millimeters, the load force in Newtons, and the system efficiency to calculate the torque needed to drive the leadscrew.
Belt & Pulley Tab: Enter the drive pulley diameter, the driven pulley diameter, and the input torque in N⋅m. The calculator will find the output torque and the pulley ratio. For bicycle applications, our bike gear ratio calculator works on the same principle of mechanical advantage through different-sized gears.
Rack & Pinion Tab: Enter the pinion radius in millimeters, the linear force in Newtons, and the system efficiency to find the torque at the pinion gear.
Multiple Forces Tab: Enter the force, distance, angle, and direction for each force acting on the system. Click "+ Add Force" to include more forces, and the calculator will find the net torque.
Results: After clicking "Calculate," the results display in both Imperial (lb⋅ft, lb⋅in) and Metric (N⋅m, N⋅mm) units, along with a vector diagram that shows the force, lever arm, angle, and torque direction.
What Is Torque?
Torque is a turning force. When you push a door open, twist a wrench, or pedal a bicycle, you are applying torque. It measures how much a force causes an object to rotate around a point, called the pivot or axis. Torque is one of the most important ideas in mechanics because it explains how and why things spin.
How Torque Is Calculated
The basic formula for torque is τ = r × F × sin(θ), where τ (the Greek letter tau) is the torque, r is the distance from the pivot point to where the force is applied (called the lever arm), F is the amount of force, and θ is the angle between the force and the lever arm. When the force pushes straight sideways at 90 degrees, sin(θ) equals 1, and you get the maximum torque. If the force pushes along the lever arm at 0 degrees, sin(θ) equals 0, and there is no torque at all — the object won't rotate. You can use our force calculator to find the applied force from Newton's second law, or our acceleration calculator to determine how that force relates to changes in motion.
Units of Torque
Torque is measured in different units depending on where you live and what field you work in. The standard SI unit is the newton-meter (N·m). In the United States and in automotive work, pound-feet (lb·ft) and pound-inches (lb·in) are common. These units all represent the same thing: a force acting at a certain distance from a pivot point.
Torque in Everyday Life and Engineering
Torque shows up everywhere. When you tighten a bolt with a wrench, the longer the wrench handle, the more torque you create with the same effort. This is why mechanics use long-handled breaker bars for stubborn lug nuts. Car engines are rated by their torque output because it tells you how much twisting power the engine can deliver to the wheels. Electric motors, wind turbines, and even simple seesaws all depend on torque. In automotive engineering, torque is closely tied to horsepower, and understanding the compression ratio of an engine helps explain how torque is generated during combustion.
Torque and Rotational Power
Torque and power are closely related. Power tells you how fast work gets done, while torque tells you how strong the turning force is. The formula that links them is P = τ × ω, where P is power in watts, τ is torque in newton-meters, and ω (omega) is the rotational speed in radians per second. A motor with high torque but low speed can produce the same power as a motor with low torque but high speed. Our horsepower calculator is especially useful for converting between torque-based power measurements in automotive and industrial contexts.
Mechanical Systems That Use Torque
Many mechanical systems are designed to change torque from one value to another. A belt and pulley system uses different-sized pulleys to multiply or reduce torque. A larger driven pulley increases the output torque compared to the input. A rack and pinion converts rotational torque into straight-line (linear) force, and is used in car steering systems. A leadscrew converts rotational motion into precise linear motion, commonly found in 3D printers and CNC machines. In each of these systems, efficiency matters — friction and other losses mean the actual output torque is always less than the ideal value. The concept of energy transfer in these systems is closely related to both kinetic energy and potential energy, since torque does work by converting one form of energy into another.
Net Torque and Multiple Forces
When more than one force acts on an object, each force creates its own torque. Some may push clockwise while others push counterclockwise. The net torque is the sum of all individual torques, taking direction into account. If the net torque is zero, the object is in rotational equilibrium and will not start spinning. This principle is the basis for balancing beams, designing bridges, and analyzing any structure that could rotate. Net torque is also directly related to angular acceleration through the moment of inertia — the rotational equivalent of mass. Just as a net force causes linear acceleration (which you can explore with our acceleration calculator), a net torque causes angular acceleration, and the resulting change in rotational momentum follows from the impulse delivered over time.