Torque Calculator Guide: Force, Distance and Rotational Motion
Quick Answer
- *Torque = Force × Distance from pivot: τ = F × d × sin(θ)
- *The SI unit is newton-meters (N·m). The US customary unit is foot-pounds (ft·lbs).
- *Doubling the lever arm length doubles the torque for the same applied force.
- *A typical car engine produces 150–300 N·m of torque; electric vehicles can exceed 1,000 N·m.
What Is Torque?
Torque is the rotational equivalent of linear force. When you push open a door, turn a wrench, or pedal a bicycle, you're applying torque. It measures how effectively a force causes an object to rotate around a pivot point (also called the axis of rotation).
The word comes from the Latin torquere, meaning “to twist.” According to MIT's Department of Physics, torque is one of the fundamental concepts in classical mechanics and is essential for analyzing any system with rotational motion.
The Torque Formula
The general formula for torque is:
τ = F × d × sin(θ)
Where:
- τ (tau) = torque, measured in N·m or ft·lbs
- F = applied force in newtons (N) or pounds (lbs)
- d = distance from the pivot point (lever arm) in meters or feet
- θ = angle between the force vector and the lever arm
When force is applied perpendicular to the lever arm (θ = 90°), sin(90°) = 1 and the formula simplifies to τ = F × d. This is the most common scenario in practical applications.
Worked Example: Tightening a Bolt
You apply 80 N of force to a 0.25 m wrench at 90°:
τ = 80 N × 0.25 m × sin(90°)
τ = 80 × 0.25 × 1
τ = 20 N·m
Our torque calculator handles these calculations instantly, including angle adjustments and unit conversions.
Torque Units and Conversions
Different industries and regions use different torque units. The most common conversions:
| From | To | Multiply By |
|---|---|---|
| N·m | ft·lbs | 0.7376 |
| ft·lbs | N·m | 1.3558 |
| N·m | in·lbs | 8.8507 |
| kgf·cm | N·m | 0.0981 |
| N·m | kgf·m | 0.1020 |
According to NIST (National Institute of Standards and Technology), the newton-meter is the only SI-recognized unit for torque. However, automotive and aerospace industries in the US predominantly use foot-pounds.
How Lever Arm Length Affects Torque
The relationship between lever arm length and torque is linear. Double the distance, double the torque. This is why Archimedes reportedly said, “Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.”
| Wrench Length | Force Applied | Torque Output |
|---|---|---|
| 6 in (0.15 m) | 100 N | 15 N·m |
| 12 in (0.30 m) | 100 N | 30 N·m |
| 18 in (0.46 m) | 100 N | 46 N·m |
| 24 in (0.61 m) | 100 N | 61 N·m |
This principle is used everywhere in engineering. The Society of Automotive Engineers (SAE) notes that breaker bars are typically 18–24 inches long specifically because longer lever arms produce more torque without requiring more physical effort.
Torque in the Real World
Automotive Engines
Engine torque determines pulling power and acceleration. According to Car and Driver (2025), peak torque figures for popular vehicles include:
- Toyota Camry 2.5L: 236 N·m (174 ft·lbs)
- Ford F-150 3.5L EcoBoost: 570 N·m (420 ft·lbs)
- Tesla Model S Plaid: 1,050 N·m (774 ft·lbs) — instant delivery
- Cummins 6.7L Diesel (Ram 3500): 1,356 N·m (1,000 ft·lbs)
Electric motors produce maximum torque at 0 RPM, which is why EVs feel so quick off the line compared to internal combustion engines that reach peak torque at 2,000–5,000 RPM.
Bicycle Pedaling
A cyclist applies roughly 150–250 N of force to a 170 mm crank arm, producing 25–42 N·m of torque per pedal stroke. Professional cyclists in the Tour de France can sustain over 400 watts for hours, translating to significantly higher torque values at lower cadences.
Industrial Applications
Wind turbines convert aerodynamic torque into electricity. According to the U.S. Department of Energy, a modern 3 MW offshore turbine produces roughly 1.5 million N·m of torque at its main shaft — enough force to lift a fully loaded school bus.
Torque vs Horsepower
Torque and horsepower are related but measure different things. Torque is the twisting force at any instant. Horsepower measures how quickly that torque is applied over time.
The relationship: HP = Torque (ft·lbs) × RPM ÷ 5,252
This means torque and horsepower always cross at 5,252 RPM on a dyno chart. Below that RPM, torque is higher; above it, horsepower is higher. Practically speaking, torque determines how hard a vehicle pulls (towing, hill climbing) while horsepower determines top speed.
Torque Wrenches and Fastener Specs
Over-tightening bolts can strip threads or crack components. Under-tightening risks loosening under vibration. The Automotive Service Excellence (ASE) certification program emphasizes that following manufacturer torque specifications is critical for safety.
| Application | Typical Torque Spec |
|---|---|
| Spark plugs (aluminum head) | 15–20 N·m |
| Wheel lug nuts (passenger car) | 100–140 N·m |
| Cylinder head bolts | 60–100 N·m |
| Structural steel bolts (A325) | 180–350 N·m |
Calculate torque for any force and distance
Use our free Torque Calculator →Need unit conversions? Try our Torque Converter
Frequently Asked Questions
What is the formula for torque?
Torque equals force multiplied by the perpendicular distance from the pivot point: τ = F × d × sin(θ). When force is applied at 90 degrees to the lever arm, sin(θ) = 1 and the formula simplifies to τ = F × d. The SI unit is newton-meters (N·m).
What is the difference between torque and force?
Force causes linear (straight-line) motion, while torque causes rotational motion around a pivot point. Torque depends on both the magnitude of the force and the distance from the pivot. A small force applied far from the pivot can produce the same torque as a large force applied close to it.
Why does a longer wrench make bolts easier to turn?
A longer wrench increases the lever arm distance (d) in the torque equation τ = F × d. Doubling the wrench length doubles the torque for the same applied force. This is why mechanics use breaker bars (often 18–24 inches) for stubborn bolts instead of standard 10-inch wrenches.
What units is torque measured in?
The SI unit for torque is the newton-meter (N·m). In the US customary system, torque is commonly measured in foot-pounds (ft·lbs) or inch-pounds (in·lbs). To convert: 1 N·m = 0.7376 ft·lbs, and 1 ft·lb = 1.3558 N·m.
How much torque does a car engine produce?
A typical passenger car produces 150–300 N·m (110–220 ft·lbs) of torque. A Ford F-150 with the 3.5L EcoBoost produces 570 N·m (420 ft·lbs). Heavy-duty diesel trucks can exceed 1,350 N·m (1,000 ft·lbs). Electric vehicles like the Tesla Model S Plaid produce 1,050 N·m (774 ft·lbs) of instant torque.