Torque is the rotational equivalent of linear force: τ = r × F × sin(θ), measuring tendency to rotate an object around a pivot.

Torque Calculator | τ = rF sin(θ)

Calculate torque from force, distance, and angle of application.

Solve For

Force (N)

Lever Arm (m)

Angle (°)

Output Unit

Also calculate shaft power (P = τ·ω)

What Is the Torque Calculator | τ = rF sin(θ)?

Torque is the rotational equivalent of linear force, it measures how much a force tends to rotate an object around a pivot point. Torque depends on three factors: the magnitude of the force, the length of the lever arm (moment arm), and the angle between force and lever arm.

The Sine Factor

›Maximum torque occurs when force is perpendicular to the lever arm (θ = 90°, sin 90° = 1)
›Zero torque occurs when force is parallel to the lever arm (θ = 0° or 180°)
›This is why wrenches are held perpendicular to the bolt, maximum rotational effectiveness
›Supplementary angles give the same torque: sin(30°) = sin(150°) = 0.5

Shaft Power Connection

›Power = torque × angular velocity: P = τ × ω
›Angular velocity ω = 2π × RPM / 60 (rad/s)
›At 1,500 RPM: ω = 157.08 rad/s; 200 N·m torque produces 31.4 kW (42.1 hp)
›Maximum torque and maximum power occur at different RPMs for most engines

Formula

Torque

τ = r × F × sin(θ)

Force

F = τ / (r × sin θ)

Lever Arm

r = τ / (F × sin θ)

Angle

θ = arcsin(τ / (r × F))

Shaft Power

P = τ × ω = τ × (2π × RPM / 60)

kW → hp

P(hp) = P(kW) × 1.341

How to Use

1Select what to solve: Torque (τ), Force (F), Lever Arm (r), or Angle (θ).
2Enter the known values in the three input fields (labels change based on solve-for mode).
3Select the desired torque unit (N·m, lb·ft, kN·m, etc.).
4For torque mode: toggle "Calculate shaft power" and enter RPM to get power in kW and hp.
5Click Calculate, results include step-by-step working and all unit conversions.
6The Torque Reference bar chart compares your result to real-world benchmarks.

Example Calculation

Tightening a lug nut: F = 150 N, lever arm r = 0.4 m, angle θ = 90°:

τ = r × F × sin(θ) = 0.4 m × 150 N × sin(90°) = 0.4 × 150 × 1 = 60 N·m Unit conversions: 60 N·m = 44.25 lb·ft 60 N·m = 6,000 N·cm 60 N·m = 0.06 kN·m

Real-World Context

60 N·m, typical car wheel lug nuts are specified at 80–120 N·m. Using a 0.4 m wrench with 150 N of force barely meets the lower bound. Always use a calibrated torque wrench for safety-critical fasteners.

Understanding Torque | τ = rF sin(θ)

Torque Unit Conversion Table

Unit	N·m	lb·ft	lb·in	kg·m	kN·m
1 N·m	1	0.7376	8.8507	0.10197	0.001
1 lb·ft	1.3558	1	12	0.13826	0.0014
1 lb·in	0.11298	0.0833	1	0.01152	0.000113
1 kg·m	9.80665	7.233	86.796	1	0.00981
1 kN·m	1,000	737.56	8,851	101.97	1
10 N·m	10	7.376	88.51	1.0197	0.01
100 N·m	100	73.76	885.1	10.197	0.1
1000 N·m	1,000	737.6	8,851	101.97	1

Frequently Asked Questions

What is torque?

Torque (τ) is the rotational effect of a force applied at a distance from a pivot:

›Formula: τ = r × F × sin(θ), where r is lever arm, F is force, θ is the angle between them
›SI unit: Newton-metres (N·m); US unit: pound-feet (lb·ft)
›Turning a wrench, spinning a wheel, and tightening a bolt all involve torque
›Torque is a vector, it has both magnitude and a rotational direction (clockwise or counterclockwise)

Why does angle matter in torque calculations?

›The sin(θ) factor extracts only the perpendicular component of force
›At 90°: sin = 1 → 100% of force creates torque (maximum)
›At 0° or 180°: sin = 0 → force is along the lever arm → zero torque
›At 45°: sin = 0.707 → only 70.7% of applied force contributes to rotation

What is the difference between N·m and lb·ft?

›1 N·m = 0.7376 lb·ft; 1 lb·ft = 1.3558 N·m
›N·m is the SI unit used globally in science and engineering specifications
›lb·ft (pound-foot) is common in US automotive manuals, torque wrenches, and specs
›lb·in (pound-inch) is used for smaller fasteners, 1 lb·in = 0.11298 N·m

How is torque related to power?

›P = τ × ω, where ω = 2π × RPM / 60 (angular velocity in rad/s)
›300 N·m at 3,000 RPM: ω = 314.16 rad/s → P = 300 × 314.16 / 1000 = 94.25 kW = 126 hp
›Same torque at higher RPM = more power, peak power RPM is always above peak torque RPM
›This is why diesel trucks (high torque, low RPM) feel different to pull away vs. sports cars (high RPM power)

What is a torque wrench and why is it important?

›A torque wrench clicks or breaks-over when the preset torque is reached
›Under-torquing: fastener works loose under vibration, can be dangerous (wheel lug nuts)
›Over-torquing: stretches or strips threads, cracks cylinder heads, distorts flanges
›Critical applications: lug nuts (80–120 N·m), spark plugs (20–30 N·m), cylinder head bolts (60–80 N·m)

What is the supplementary angle in the solve-for-angle result?

›sin(30°) = sin(150°) = 0.5, both angles produce the same torque for given r and F
›The calculator shows both the primary angle and its supplement (180° − θ)
›Choose the physically meaningful solution based on your setup
›In most real applications θ is between 0° and 90°, the primary solution is usually correct

How do I convert torque between imperial and metric units?

›1 lb·ft = 1.3558 N·m | 1 N·m = 0.7376 lb·ft
›1 lb·in = 0.11298 N·m | 12 lb·in = 1 lb·ft
›1 kg·m = 9.80665 N·m (using g = 9.80665 m/s²)
›The calculator displays all six unit conversions simultaneously when solving for torque

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