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Torque Calculator

torque calculator. Get instant, accurate results. Enter values for instant results with step-by-step formulas.

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Physics

Torque Calculator

Free online torque calculator. Get instant, accurate results.

Last updated: December 2025

Calculator

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Formula

τ = r × F × sin(θ)

Rotational force. Torque equals the cross product of position vector and force.

Last reviewed: December 2025

Worked Examples

Example 1: Wrench

50 N force, 0.5 m handle, 90°
Solution:
τ=0.5×50×sin(90°)=25 N·m
Result: 25 N·m
Expert Insights

Background & Theory

The Torque Calculator applies the following established principles and formulas. Physics is the fundamental natural science concerned with matter, energy, and the interactions between them. Classical mechanics, founded on Newton's three laws of motion, provides the framework for analyzing the motion of objects. The first law states that an object remains at rest or in uniform motion unless acted upon by a net external force. The second law quantifies this relationship: F = ma, where force equals mass times acceleration in SI units of newtons (N = kg·m/s²). The third law establishes that every action produces an equal and opposite reaction. Kinematics describes motion without reference to its causes. The four fundamental equations relate displacement s, initial velocity u, final velocity v, acceleration a, and time t: v = u + at, s = ut + ½at², v² = u² + 2as, and s = ½(u + v)t. These assume constant acceleration and are foundational for solving projectile motion, free fall, and linear dynamics problems. Energy conservation underpins much of physics. Kinetic energy is KE = ½mv², where m is mass in kilograms and v is speed in meters per second. Gravitational potential energy is PE = mgh, where g ≈ 9.81 m/s² near Earth's surface and h is height in meters. The work-energy theorem states that the net work done on an object equals its change in kinetic energy: W = ΔKE. Electricity and circuits rely on Ohm's law: V = IR, where voltage V is in volts, current I in amperes, and resistance R in ohms. Electrical power is P = IV = I²R = V²/R, measured in watts. Wave mechanics connects frequency f, wave speed v, and wavelength λ through f = v/λ, with frequency in hertz (Hz). Pressure is defined as force per unit area, P = F/A, in pascals (Pa = N/m²). The ideal gas law PV = nRT links pressure, volume, moles n, the gas constant R = 8.314 J/(mol·K), and absolute temperature in kelvin. Gravitational force between two masses follows Newton's law of universal gravitation: F = Gm₁m₂/r², where G = 6.674×10⁻¹¹ N·m²/kg² is the gravitational constant.

History

The history behind the Torque Calculator traces back through the following developments. The history of physics spans over two millennia, beginning with the natural philosophy of ancient Greece. Aristotle (384–322 BCE) proposed that all matter consisted of four elements and that objects moved toward their natural place, with heavier objects falling faster than lighter ones. While largely incorrect, his systematic approach to explaining nature dominated Western thought for nearly 2,000 years. The Scientific Revolution overturned Aristotelian physics. Galileo Galilei (1564–1642) performed groundbreaking experiments on inclined planes and falling bodies, demonstrating that all objects fall with the same acceleration regardless of mass, and established the principle of inertia. His use of mathematics to describe motion was revolutionary. Isaac Newton synthesized these developments in his landmark Principia Mathematica (1687), laying out the three laws of motion and the law of universal gravitation. Newton's framework unified terrestrial and celestial mechanics, explaining planetary orbits with the same equations governing a falling apple. His calculus provided the mathematical language for expressing rates of change. The 19th century brought two major theoretical achievements. James Clerk Maxwell formulated his equations of electromagnetism between 1861 and 1862, unifying electricity, magnetism, and optics, and predicting the existence of electromagnetic waves traveling at the speed of light. Thermodynamics was developed by Carnot, Clausius, and Kelvin, establishing the laws governing heat, work, and entropy. The 20th century produced two revolutions that fundamentally altered the classical picture. Albert Einstein published the special theory of relativity in 1905, showing that space and time are not absolute but relative to the observer, and that mass and energy are equivalent via E = mc². His general theory of relativity in 1915 reinterpreted gravity as the curvature of spacetime. Simultaneously, quantum mechanics emerged from the work of Planck, Bohr, Heisenberg, and Schrödinger, revealing that at atomic scales energy is quantized and particles exhibit wave-particle duality. These developments culminated in the Standard Model of particle physics, which describes all known fundamental particles and three of the four fundamental forces.

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Frequently Asked Questions

Torque (τ) is the rotational equivalent of force. It measures how effectively a force causes an object to rotate about an axis: τ = r × F × sin(θ), where r is the lever arm length, F is the applied force, and θ is the angle between r and F. The SI unit is Newton-metres (N·m).
Use τ = r × F × sin(θ). Maximum torque occurs at θ = 90° (sin 90° = 1). Example: a 50 N force applied at 0.4 m from the pivot at 60°: τ = 0.4 × 50 × sin(60°) = 0.4 × 50 × 0.866 ≈ 17.3 N·m.
Force F is in Newtons (N), lever arm r in metres (m), and angle θ in degrees (converted internally to radians). Torque τ is in Newton-metres (N·m). In imperial units, 1 N·m = 0.7376 ft·lbf. Automotive specs often use N·m or lb·ft.
Power equals torque multiplied by angular velocity: P = τω, where ω is in radians per second. In practical terms: Power (W) = Torque (N·m) × 2π × RPM / 60. For cars: HP ≈ Torque (lb·ft) × RPM / 5252. A 300 lb·ft engine at 4000 RPM produces about 228 HP.
You may use the results for reference and educational purposes. For professional reports, academic papers, or critical decisions, we recommend verifying outputs against peer-reviewed sources or consulting a qualified expert in the relevant field.
All calculations use established mathematical formulas and are performed with high-precision arithmetic. Results are accurate to the precision shown. For critical decisions in finance, medicine, or engineering, always verify results with a qualified professional.
Educational Note: This calculator is provided for educational and informational purposes. Results are based on the formulas and inputs provided. Always verify important calculations independently. NovaCalculator processes calculator inputs client-side; optional analytics follow visitor consent settings. © 2024–2026 NovaCalculator.

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Formula

τ = r × F × sin(θ)

Rotational force. Torque equals the cross product of position vector and force.

Frequently Asked Questions

What is the difference between horsepower and torque?

Horsepower measures how quickly work is done (sustained speed and acceleration at higher RPMs). Torque measures rotational force (pulling power and low-end acceleration). Diesel trucks emphasize torque for towing. Sports cars emphasize horsepower for top speed. HP = torque x RPM / 5,252.

How do I interpret the result?

Results are displayed with a label and unit to help you understand the output. Many calculators include a short explanation or classification below the result (for example, a BMI category or risk level). Refer to the worked examples section on this page for real-world context.

How do I get the most accurate result?

Enter values as precisely as possible using the correct units for each field. Check that you have selected the right unit (e.g. kilograms vs pounds, meters vs feet) before calculating. Rounding inputs early can reduce output precision.

Does Torque Calculator work offline?

Once the page is loaded, the calculation logic runs entirely in your browser. If you have already opened the page, most calculators will continue to work even if your internet connection is lost, since no server requests are needed for computation.

Is my data stored or sent to a server?

No. All calculations run entirely in your browser using JavaScript. No data you enter is ever transmitted to any server or stored anywhere. Your inputs remain completely private.

Can I use Torque Calculator on a mobile device?

Yes. All calculators on NovaCalculator are fully responsive and work on smartphones, tablets, and desktops. The layout adapts automatically to your screen size.

Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy