Torque Calculator
Three-mode torque calculator: find torque from force and lever arm, convert to mechanical power, or compute from moment of inertia. Full unit conversion included.
What is Torque?
Torque (also called a moment of force) is the rotational equivalent of linear force. It measures how effectively a force causes an object to rotate about a pivot point or axis. The Greek letter τ (tau) is the standard symbol.
The fundamental formula is:
τ = F × r × sin(θ)
where F is the applied force, r is the length of the lever arm (the distance from the pivot to where the force is applied), and θ is the angle between the force vector and the lever arm. Torque is maximized when the force is perpendicular to the arm (θ = 90°, sin θ = 1).
The SI unit of torque is the newton-metre (N·m). In US engineering, pound-feet (lb·ft) is common for engine and bolt specifications. Note that N·m and joules are dimensionally identical, but torque is a vector quantity (it has a direction, given by the right-hand rule) while energy is a scalar.
Torque is fundamental in mechanical engineering: engine design, bolt tightening, gear systems, structural moment analysis, and all rotating machinery involve torque calculations.
Formula
Torque from force and lever arm: τ = F × r × sin(θ)
Power from torque and speed: P = τ × ω = τ × 2π × RPM / 60
Rotational Newton’s Second Law: τ = I × α
Variables:
- τ — torque (N·m or lb·ft)
- F — applied force (N, kN, or lbf)
- r — lever arm length (m, cm, mm, ft, or in)
- θ — angle between force and arm (degrees)
- P — power (W, kW, or hp)
- ω — angular velocity (rad/s) = 2π × RPM / 60
- I — moment of inertia (kg·m²)
- α — angular acceleration (rad/s²)
How to Use
- Torque from Force mode — enter force F, lever arm r, and angle θ. Choose units for force (N, kN, lbf) and arm length (m, cm, mm, ft, in). Select an output unit (N·m, lb·ft, kN·m, etc.) and click Calculate.
- Torque to Power mode — enter torque τ and rotational speed in RPM. The calculator computes angular velocity ω = 2π × RPM / 60, then power P = τω. Output shown in W, kW, and hp simultaneously.
- Rotational Second Law mode — enter moment of inertia I and angular acceleration α. The calculator returns the net torque τ = Iα and its direction (positive = counterclockwise, negative = clockwise).
- Read all unit conversions — every result shows the value in the selected unit plus common alternatives (N·m and lb·ft for torque, W/kW/hp for power).
- Check the steps — the working panel shows every conversion and formula step.
Example Calculations
Example 1 — Torque from Force at 90°
Wrench: 100 N applied at 0.5 m, perpendicular (θ = 90°)
1
sin(90°) = 1 (force is perpendicular to lever arm — maximum torque)
2
τ = F × r × sin(θ) = 100 × 0.5 × 1 = 50 N·m
Torque = 50 N·m = 50 × 0.7376 = 36.88 lb·ft
Try this example →Example 2 — Engine Torque to Power
Engine producing 200 N·m at 3,000 RPM
1
ω = 2π × 3000 / 60 = 2π × 50 = 314.16 rad/s
2
P = τ × ω = 200 × 314.16 = 62,832 W = 62.8 kW
3
62,832 W × 0.001341 = 84.2 hp
Power = 62.8 kW / 84.2 hp at 3,000 RPM with 200 N·m torque
Try this example →Example 3 — Torque from Moment of Inertia
Flywheel: I = 2 kg·m², α = 5 rad/s²
1
τ = I × α = 2 × 5 = 10 N·m
2
10 N·m = 10 × 0.7376 = 7.376 lb·ft
Required torque = 10 N·m to accelerate the flywheel at 5 rad/s²
Try this example →❓ Frequently Asked Questions
What is torque and how is it different from force?
Force is a linear push or pull (measured in newtons). Torque is the rotational effect of a force about a pivot point (measured in N·m). The same force produces more torque with a longer lever arm: τ = F × r × sin(θ). A 100 N force at 0.5 m produces 50 N·m of torque; at 1 m it produces 100 N·m. Torque determines how quickly something rotates or resists rotation.
What is the formula for torque?
τ = F × r × sin(θ), where F is the applied force, r is the lever arm length (pivot to force application point), and θ is the angle between the force direction and the lever arm. Maximum torque occurs at θ = 90° (force perpendicular to arm). At θ = 0° or 180°, the force acts through the pivot and no torque is produced.
How do you convert torque to power?
P = τ × ω, where ω is angular velocity in rad/s. Convert RPM to rad/s: ω = 2π × RPM / 60. Example: 300 N·m at 2000 RPM: ω = 2π × 2000/60 = 209.4 rad/s, P = 300 × 209.4 = 62,832 W ≈ 62.8 kW. In imperial units: hp = (lb·ft × RPM) / 5252.
How do you convert N·m to lb·ft?
1 N·m = 0.737562 lb·ft. To convert: lb·ft = N·m × 0.7376. To convert the other way: N·m = lb·ft / 0.7376 = lb·ft × 1.35582. Example: 250 N·m = 250 × 0.7376 ≈ 184.4 lb·ft. A torque wrench set to 100 lb·ft = 100 / 0.7376 ≈ 135.6 N·m.
What is moment of inertia and how does it relate to torque?
Moment of inertia I is the rotational analogue of mass — it measures resistance to angular acceleration. τ = I × α is Newton’s second law for rotation, analogous to F = ma. For a solid disk: I = ½mr². For a thin ring: I = mr². Distributing mass further from the axis increases I, requiring more torque for the same angular acceleration (and storing more rotational kinetic energy).
What is the torque wrench tightening spec for common bolts?
Typical tightening torques: M6 bolt (grade 8.8) ≈ 9 N·m, M8 ≈ 22 N·m, M10 ≈ 43 N·m, M12 ≈ 75 N·m, M16 ≈ 180 N·m, M20 ≈ 360 N·m. Always check manufacturer specifications — actual values depend on bolt grade, thread pitch, lubrication, and joint material. Over-tightening yields the bolt; under-tightening risks loosening under vibration.
What is the right-hand rule for torque direction?
Torque is a vector quantity. Its direction is given by the right-hand rule: curl the fingers of your right hand from the lever arm vector r toward the force vector F; the thumb points in the direction of the torque vector. Counterclockwise rotation (viewed from above) gives positive torque; clockwise gives negative. The torque vector lies along the axis of rotation, perpendicular to both r and F.
How does gear ratio affect torque?
A gear pair multiplies torque inversely to speed: output torque = input torque × gear ratio. A 4:1 gear ratio gives 4× the input torque at 1/4 the speed (ignoring friction). This is why first gear in a car (high gear ratio) gives high torque for acceleration, while fifth gear (low gear ratio) gives low torque but high speed for cruising. Power = torque × angular velocity is conserved (minus friction losses).
What is the difference between torque and moment?
In engineering, “torque” and “moment of force” are often used interchangeably. A subtle distinction: torque typically refers to the twisting moment in a shaft or rotating machine, while “moment” is used more broadly for the bending moment in a beam (which causes bending, not rotation). Both are F × r, but the context and resulting deformation differ. Structural engineers favor “moment”; mechanical engineers favor “torque”.
What is angular acceleration and how is it measured?
Angular acceleration α is the rate of change of angular velocity ω: α = dω/dt, measured in radians per second squared (rad/s²). For uniform angular acceleration: ω = ω⊂0; + αt and θ = ω⊂0;t + ½αt² (rotational kinematics, analogous to linear). A motor accelerating from 0 to 3000 RPM in 2 seconds has α = (3000 × 2π/60 − 0) / 2 = 314.16 / 2 = 157.1 rad/s².