🔬 Torque Calculator

Torque is the rotational equivalent of force—it measures how effectively a force causes an object to rotate about a pivot point. The formula τ = r × F × sin(θ) gives the torque in newton-metres (N·m), where r is the distance from the pivot to the point of force application, F is the applied force, and θ is the angle between the force direction and the lever arm. When the force is perpendicular to the lever (θ = 90°), this simplifies to τ = r × F.

From tightening a bolt with a wrench to the spinning of electric motors, torque governs all rotational motion. This calculator solves for any one unknown (τ, r, or F) when the other two are given, assuming a 90° angle for simplicity. For angled forces, use the full τ = rF sin(θ) formula.

The calculator uses τ = r × F (assuming perpendicular force). A longer wrench arm or greater force produces more torque—the reason a cheater bar helps loosen stubborn bolts. The relationship is linear: doubling the arm length doubles the torque.

Torque and power are related: P = τ × ω, where ω is the angular velocity in rad/s. This is why car engines specify both peak torque and peak horsepower.

1. Enter any two of the three values: Torque (τ), Force (F), or Lever Arm (r).
2. Leave the third field blank—that is what will be calculated.
3. Click the Calculate button.
4. Review the result for the unknown value.

What is the difference between torque and force?

Force causes linear acceleration (F = ma). Torque causes rotational acceleration (τ = Iα, where I is moment of inertia). Torque depends on both the force and the distance from the pivot—a small force at a large distance can equal a large force at a small distance.

What units should I use?

SI units: force in newtons (N), distance in metres (m), torque in newton-metres (N·m). Imperial alternatives: force in pounds-force (lbf), distance in feet (ft), torque in foot-pounds (ft·lbf). Use consistent units throughout.

How does torque relate to horsepower?

Power = Torque × Angular Velocity: P = τω. In imperial units, HP = (Torque × RPM) / 5252. An engine with high torque at low RPM feels powerful off the line; high horsepower at high RPM means strong top-speed performance.

Why is a longer wrench better?

Torque = force × distance. A longer handle (larger r) produces more torque for the same force. This is why breaker bars and cheater pipes are used to loosen very tight bolts—you trade extra distance for less required force.

What happens if I apply force at an angle?

Only the perpendicular component of force creates torque: τ = rF sin(θ). At 90°, sin(90°) = 1 (maximum torque). At 0° or 180°, sin = 0 (no torque). This is why pushing a door at 90° to its surface is most effective.

What is the torque specification for car wheel nuts?

Typical passenger car wheel nuts are torqued to 80-120 N·m (60-90 ft·lbf), depending on the vehicle. Over-tightening can stretch or break studs; under-tightening can cause wheels to loosen. Always use a calibrated torque wrench.

Use newtons (N) for force, metres (m) for distance, and newton-metres (N·m) for torque. This calculator assumes the force is applied at 90° to the lever arm. For other angles, multiply by sin(θ). The direction of torque (clockwise vs. counterclockwise) matters for net torque calculations: assign positive to one direction and negative to the other, then sum. For rotational equilibrium, the net torque must be zero.