Torque Calculator
Calculate torque calculator calculate rotational moment of force tau from lever arm radius r, applied force F, and angle theta (tau = r * F * sin(theta)). Accurate physics formulas and unit conversions for engineers, students & technicians.
Calculate Torque (τ = r · F · sinθ)
Enter your physical parameters below to compute verified torque metrics.
Calculation Results
Calculated using verified physical methodology: Rotational Torque: \tau = r \cdot F \cdot \sin\theta
Power-Torque Relation: P = \tau \cdot \omega
Quick Summary
The Torque Calculator computes rotational moment of force ($\tau = r \cdot F \cdot \sin\theta$) from lever arm radius, force magnitude, and angle in Newton-meters ($\text{N}\cdot\text{m}$), foot-pounds ($\text{ft}\cdot\text{lbf}$), and inch-pounds ($\text{in}\cdot\text{lbf}$).
Formula Explanation
Rotational Torque: \tau = r \cdot F \cdot \sin\theta
Power-Torque Relation: P = \tau \cdot \omega
How It Works
The Torque Calculator multiplies lever arm radius ($r$ in meters) by applied force ($F$ in Newtons) and the sine of force angle ($\sin\theta$). It outputs torque in $\text{N}\cdot\text{m}$, Imperial $\text{ft}\cdot\text{lbf}$, $\text{in}\cdot\text{lbf}$, and metric $\text{kgf}\cdot\text{m}$.
Step-by-Step Worked Example
Practical Problem: A mechanic applies a force of 200 N to a 0.5 meter long wrench at a perpendicular angle of 90.0°. Calculate output torque.
- Step 1: Identify Input Parameters: Lever Arm $r = 0.5\text{ m}$, Force $F = 200.0\text{ N}$, Angle $\theta = 90.0^\circ$.
- Step 2: Calculate Angle Sine Term ($\sin(90^\circ)$): $\sin(90^\circ) = 1.0000$.
- Step 3: Apply the Torque Formula: $\tau = r \cdot F \cdot \sin\theta$.
- Step 4: Execute Numeric Multiplication: $\tau = 0.5\text{ m} \times 200.0\text{ N} \times 1.0 = 100.00\text{ Newton-meters (N}\cdot\text{m)}$.
- Step 5: Convert and Interpret Imperial & Metric Units: Torque $\tau = 100.00\text{ N}\cdot\text{m}$. Imperial Foot-pounds: $100 \times 0.737562 = 73.76\text{ ft}\cdot\text{lbf}$. Inch-pounds: $100 \times 8.85075 = 885.08\text{ in}\cdot\text{lbf}$. Kilogram-force meters: $\100 / 9.80665 = 10.20\text{ kgf}\cdot\text{m}$. Perpendicular Force Component: $F_{\perp} = 200.0\text{ N}$.
Real-World Calculation Examples
Scenario 1: Mechanic Wrench Tightening
Parameters: $r = 0.5\text{ m}$, $F = 200\text{ N}$, $\theta = 90^\circ$
Result: $\tau = 100.00\text{ N}\cdot\text{m}$ (73.76 ft·lbf, 885 in·lbf). Wrench bolt torque.
Scenario 2: Automotive Engine Crankshaft Output
Parameters: $r = 0.08\text{ m}$ (crank throw), $F = 5,000\text{ N}$ (piston force), $\theta = 90^\circ$
Result: $\tau = 400.00\text{ N}\cdot\text{m}$ (295.02 ft·lbf). Engine crankshaft torque.
Scenario 3: Angled Pry Bar Force (45°)
Parameters: $r = 1.0\text{ m}$, $F = 500\text{ N}$, $\theta = 45^\circ$
Result: $\tau = 353.55\text{ N}\cdot\text{m}$ (260.77 ft·lbf). Angled lever torque ($\sin 45^\circ = 0.7071$).
Scenario 4: Door Handle Opening Push
Parameters: $r = 0.1\text{ m}$, $F = 20\text{ N}$, $\theta = 90^\circ$
Result: $\tau = 2.00\text{ N}\cdot\text{m}$ (1.48 ft·lbf, 17.70 in·lbf). Door handle torque.
Key Benefits of Using This Calculator
Vector Angle Sine Resolution
Adjusts torque output accurately for non-perpendicular applied force angles ($\theta$).
Power-Torque Cross Relation
Verifies mechanical engine power output relation $P = \tau \cdot \omega$.
Multi-Unit Readouts
Outputs torque in $\text{N}\cdot\text{m}$, $\text{ft}\cdot\text{lbf}$, $\text{in}\cdot\text{lbf}$, and $\text{kgf}\cdot\text{m}$.
100% Free & Client-Side
Executes locally in your browser with zero latency or web server transmission.
Frequently Asked Questions (FAQ)
What is torque in physics?
Torque (tau), also called moment of force, is a vector measure of the rotational turning force applied to an object about a pivot axis (tau = r * F * sin(theta)).
What is the formula for torque?
tau = r * F * sin(theta), where r is lever arm length in meters, F is force in Newtons, and theta is angle between lever arm and force vector.
What is the SI unit of torque?
The SI unit of torque is the Newton-meter (N·m).
How converts N·m to foot-pounds (ft·lbf)?
Multiply N·m by 0.737562 to obtain foot-pounds (ft·lbf) (e.g. 100 N·m = 73.76 ft·lbf).
How converts N·m to inch-pounds (in·lbf)?
Multiply N·m by 8.85075 to obtain inch-pounds (in·lbf) (e.g. 100 N·m = 885.08 in·lbf).
Why is perpendicular force (90 degrees) most effective?
Because sin(90°) = 1.0, which maximizes the lever arm turning effect for a given force magnitude.
When is torque equal to zero?
Torque is zero when 1) force is zero (F = 0), 2) lever arm is zero (r = 0, pushing directly at pivot), or 3) force vector points directly toward or away from pivot (theta = 0° or 180°, sin(theta) = 0).
How relates torque to engine power?
Power P = tau * omega; in Imperial units, Horsepower hp = (Torque_ft_lbf * RPM) / 5252.
What is Newton's Second Law for rotation?
Sigma tau = I * alpha, where I is moment of inertia and alpha is angular acceleration in rad/s².
What is a torque wrench used for in mechanics?
A torque wrench measures exact tightening torque applied to threaded fasteners to meet engineering bolt tension specifications without stripping threads.