Work Calculator

Calculate work done by a force. Enter force, distance, and angle between force and displacement to determine work energy.

Work Formula: W = F * d * cos(?) Where: ? W = Work (Joules, J) ? F = Force applied (Newtons, N) ? d = Displacement/Distance (meters, m) ? ? = Angle between force and displacement (degrees) Special Cases: ? ? = 0deg (parallel): W = F * d (maximum work) ? ? = 90deg (perpendicular): W = 0 (no work) ? ? = 180deg (opposite): W = -F * d (negative work) Unit Conversions: ? 1 J = 1 N*m = 1 kg*m^2/s^2 ? 1 J = 0.7376 ft*lb ? 1 kJ = 1000 J ? 1 ft*lb = 1.356 J Work-Energy Theorem: ? W_net = DeltaKE = ?m(v_f^2 - v_i^2) ? Work against gravity: W = mgh
Example 1 - Pushing a Box (parallel): Force = 50 N, Distance = 10 m, Angle = 0deg W = 50 * 10 * cos(0deg) = 50 * 10 * 1 = 500 J Positive work: 500 J energy transferred to box. Example 2 - Pulling at an Angle: Force = 100 N, Distance = 5 m, Angle = 30deg W = 100 * 5 * cos(30deg) = 100 * 5 * 0.866 = 433 J Only the horizontal component (86.6 N) does work. Example 3 - Lifting (vertical): Force = 200 N, Distance = 3 m, Angle = 0deg W = 200 * 3 * 1 = 600 J = 442.5 ft*lb Work done against gravity: 600 J. Example 4 - Friction (opposing motion): Force = 40 N (friction), Distance = 8 m, Angle = 180deg W = 40 * 8 * cos(180deg) = 40 * 8 * (-1) = -320 J Negative work: friction removes 320 J energy. Example 5 - Perpendicular Force: Force = 75 N, Distance = 6 m, Angle = 90deg W = 75 * 6 * cos(90deg) = 75 * 6 * 0 = 0 J No work done (force perpendicular to motion).

What is work in physics?

Work is the energy transferred when a force moves an object. The formula is W = F * d * cos(?), where F is force, d is displacement, and ? is the angle between force and displacement. Work is measured in Joules (J), where 1 J = 1 N*m.

Why does angle matter in work calculations?

Only the component of force in the direction of motion does work. If force is parallel to motion (?=0deg), cos(0deg)=1, so W=F*d. If perpendicular (?=90deg), cos(90deg)=0, so W=0 (no work). At other angles, cos(?) gives the effective force component.

What is positive work vs negative work?

Positive work (W>0) occurs when force aids motion (0deg=?<90deg), adding energy to the object. Negative work (W<0) occurs when force opposes motion (90deg<?=180deg), removing energy. Example: lifting = positive work, friction = negative work.

When is no work done?

No work is done when: (1) force is perpendicular to displacement (?=90deg), like centripetal force in circular motion; (2) there's no displacement (d=0), like pushing a wall that doesn't move; (3) there's no force (F=0).

What are common units for work and energy?

SI unit: Joule (J) = N*m = kg*m^2/s^2. Other units: kilojoule (kJ) = 1000 J, foot-pound (ft*lb), calorie (cal), kilocalorie (kcal or Cal), electron-volt (eV). Conversions: 1 J = 0.738 ft*lb, 1 ft*lb = 1.356 J.

How does work relate to energy?

The Work-Energy Theorem states that net work equals change in kinetic energy: W_net = DeltaKE = ?m(v_f^2 - v_i^2). Work transfers energy between objects or converts it between forms (kinetic, potential, thermal). Energy conservation: work done = energy transferred.

What is the difference between work and power?

Work is total energy transferred (measured in Joules). Power is the rate of doing work: P = W/t (measured in Watts). Example: lifting 100 kg 2 m does ~1960 J of work whether it takes 1 second (1960 W power) or 10 seconds (196 W power).

Can work be done by multiple forces?

Yes. Calculate work for each force separately, then add algebraically (considering signs). Net work = W_1 + W_2 + ... Total work equals work done by net force: W_net = F_net * d * cos(?). Example: car moving with engine force (+) and friction (-).

What are real-world examples of work calculations?

Examples: lifting objects (W = mgh), pulling a sled (W = F*d*cos(?)), compressing a spring (W = ?kx^2), braking a car (negative work by friction), pumping water uphill, loading cargo, and construction equipment operations.

How do I calculate work done against gravity?

For vertical lifting: W = mgh, where m is mass, g is gravitational acceleration (9.8 m/s^2), and h is height. This simplifies W = F*d with F = mg (weight) and d = h. Example: lifting 10 kg up 2 m requires W = 10*9.8*2 = 196 J.

What is work done by friction?

Friction always opposes motion, so ? = 180deg and cos(180deg) = -1. Work by friction: W = -f*d (always negative), where f is friction force. This removes kinetic energy, converting it to heat. Example: friction f=50 N over d=10 m does W = -500 J.

How do I convert between Joules and foot-pounds?

Conversions: 1 J = 0.737562 ft*lb, and 1 ft*lb = 1.35582 J. To convert: multiply Joules by 0.7376 to get ft*lb, or multiply ft*lb by 1.356 to get Joules. These units are common in imperial/metric engineering contexts.