Work Calculator

Work Calculator finds the work a force does from its size, distance and angle in joules or foot-pounds. It also solves for force, distance or angle and adds net work with friction.

Work Calculator for Physics Problems

The Work Calculator finds the work a force does on an object as it moves. With the loaded values of 120 N, 5 m and a 30° angle, the answer is 519.6 J. The same screen shows that 86.6% of the force acts along the motion and that 60 N of it is perpendicular.

The Calculate From list offers four starting points. Force and Displacement is the classic textbook case and can solve for any one of its four values. Mass and Acceleration builds the force first. Velocity Change uses kinetic energy, and Net Work with Friction sets a pull or a push against friction on a level floor or a slope.

Anyone searching for a work calculator in physics usually has a homework line such as “a 75 N push at 35° over 25 m”. Enter those three numbers and the result is 1,536 J. That matches the 1.54 × 10³ J printed for the same lawn mower problem in OpenStax University Physics, section 7.1.

Work Formula with an Angle

In physics, work is the energy a force transfers to an object while the object moves. A force that moves nothing does no work, however hard it pushes. For a steady force the formula for work uses the force, the displacement and the angle between them.

$$W = F \times d \times \cos\theta$$

W is the work in joules, F is the force in newtons, d is the displacement in meters and θ is the angle between the force and the direction of motion. One joule is one newton acting through one meter. When the force points straight along the motion, θ is 0° and the formula shortens to W = F × d.

To calculate work done by hand, first find the part of the force along the motion, which is F × cos θ. For 120 N at 30° that part is 103.9 N. Multiply it by the 5 m displacement and the work done is 519.6 J. The Force Diagram in the tool draws both parts of the force to scale.

A work calculator with angle input matters because the angle changes the answer more than most people expect. The table keeps 120 N and 5 m fixed and changes only θ. It is the same Work by Angle table the tool builds for your own numbers.

What is negative work done?

Work is negative when the force points against the motion, which means an angle above 90°. At 120° the same 120 N over 5 m gives −300 J. The force takes 300 J of energy out of the object instead of adding it, the way friction and braking do.

Work is zero at exactly 90°, because a force at a right angle to the motion has no part along it. The upward support on a box carried across a level floor is one example. Work is also zero when nothing moves, so holding a heavy bag still does no work in the physics sense.

Solving for Force, Distance or Angle

The Solve For list turns the work formula around. Pick Force, Displacement or Angle, and the Work Calculator shows a work field in place of the value being solved. The loaded work for these cases is 250 J.

$$F = \frac{W}{d \times \cos\theta}$$

With 250 J over 5 m at 30°, the force needed is 57.74 N. Solving for displacement with 120 N at 30° gives 2.406 m. Solving for the angle with 120 N over 5 m gives 65.38°, which the tool also prints as 1.141 rad.

$$\theta = \arccos\left(\frac{W}{F \times d}\right)$$

Some combinations have no answer, and the tool says why. A 120 N force over 5 m can do 600 J at most, so 700 J has no angle. Positive work needs an angle below 90°, and at exactly 90° no force or distance can produce any work at all.

The same rearrangement finds a stopping force. OpenStax works a 2.60 g bullet at 335 m/s that stops in 15.2 cm of wood. Its kinetic energy is 145.9 J, and dividing by 0.152 m gives an average force of about 960 N. The Bullet Energy Calculator supplies that energy figure for other loads.

Work from Mass and Acceleration

When the force is not given, it comes from Newton’s second law as mass times acceleration. The Mass and Acceleration option does both steps and then applies the same angle rule as the main formula.

$$W = m \times a \times d \times \cos\theta$$

The acceleration field loads standard gravity, 9.80665 m/s², and the angle loads 0°. With those values the force is the weight of the mass, so the result is the work of a lift. Raising 20 kg by 5 m takes 196.1 N and 980.7 J of work.

Set the angle to 30° and the same 196.1 N does 849.3 J over 5 m. The angle here must stay below 90°, because the tool also works out the speed from rest and the time to cover the distance.

This option has its own Solve For list with work, mass, acceleration and displacement. For 250 J over 5 m at 30° under standard gravity, the mass is 5.887 kg. A 20 kg mass would need 2.887 m/s² for the same work, and at standard gravity it would cover 1.472 m.

That 980.7 J is the same number as m × g × h, the gain in potential energy worked out in the Potential Energy Calculator. Gravity itself does negative work on the way up and positive work on the way down. Over a full trip up and back its total work is zero.

A stretching spring is a case this formula cannot handle, because the force grows with the stretch. Spring work is half the spring constant times the stretch squared, and the Elastic Potential Energy Calculator covers it.

Work from a Velocity Change

The work-energy theorem says the net work on an object equals the change in its kinetic energy. OpenStax section 7.3 states it as net work equal to final kinetic energy minus initial kinetic energy. No force or distance is needed, only the mass and the two speeds.

$$W = \frac{1}{2} \times m \times (v_1^2 – v_0^2)$$

A 20 kg mass that speeds up from 3 m/s to 9 m/s goes from 90 J to 810 J of kinetic energy, so the work is 720 J. Enter a time of 4 s and the Work Calculator adds the average force of 30 N and the 24 m covered. Their product is the same 720 J.

Swap the two speeds and the result is −720 J. Slowing from 9 m/s to 3 m/s removes that energy, and a brake turns it into heat. The Kinetic Energy Calculator goes further on the energy side, including solving for the speed or the mass.

How to Calculate Net Work

Net work is the total work done by every force on the object. To calculate total work, find the work of each force with its own angle and add them with their signs. Forces at 90° to the motion drop out, which on a level floor removes gravity and the normal force.

The Net Work with Friction option handles a force at an angle to the surface, on a level floor or an incline. A pull angled upward lightens the load on the floor, so the normal force and the friction both fall. A push angled downward does the opposite.

$$N = m \times g \times \cos\beta – F \times \sin\theta$$

$$W_{net} = (F \times \cos\theta – \mu \times N – m \times g \times \sin\beta) \times d$$

Here N is the normal force, μ is the kinetic friction coefficient, g is standard gravity and β is the incline angle, which is 0 on a level floor. For a push, the minus sign in the first formula becomes a plus. With a 120 N pull at 30° on a level 20 kg box, the normal force is 136.1 N, and at μ = 0.3 the friction force is 40.84 N.

Over 5 m the pull does 519.6 J and friction does −204.2 J, so the net work is 315.4 J. Friction takes 39.3% of the work put in. The 315.4 J left over becomes kinetic energy and takes the box from rest to 5.616 m/s.

Change Force Direction to a push and the same 120 N at 30° presses the box into the floor. The normal force rises to 256.1 N and friction to 76.84 N. The applied work is still 519.6 J, but the net work drops to 135.4 J and the final speed to 3.68 m/s.

Set the Incline Angle to 10° with the pull and gravity joins in. Moving 5 m up the slope, gravity does −170.3 J and friction does −199.7 J. The net work is 149.6 J and the box reaches 3.868 m/s. The incline covers motion up the slope only.

From rest the Work Calculator also checks the pull against static friction, using the second coefficient under the options bar. If the pull along the floor cannot beat it, the box does not move and no work is done. Coefficients for real surfaces come from the Friction Calculator, and the Normal Force Calculator shows the normal force on its own for other loadings.

Joules, Foot-Pounds and Other Units

The SI unit of work is the joule, which is one newton-meter. In US units it is the foot-pound, and 1 ft·lbf is 1.355818 J in NIST Special Publication 811. The loaded 519.6 J is 383.2 foot-pounds, 124.2 calories or 0.1443 watt-hours.

The Work Calculator accepts force in newtons, kilonewtons and pounds-force, with distance in meters, centimeters, kilometers, feet or inches. The Result Unit bar switches the answer between joules, kilojoules, foot-pounds, calories, kilocalories, BTU and watt-hours. The calorie used is the thermochemical one of exactly 4.184 J.

What is the SI unit of power?

Power is work divided by time, and its SI unit is the watt, which is one joule per second. The 720 J from the velocity example, done in 4 s, is 180 W. For a steady force, power is also force times speed. The three electrical formulas of power are set out with the Watt Converter.

What are the 3 Ohm’s law formulas?

Ohm’s law is V = I × R, and its other two forms are I = V ÷ R and R = V ÷ I. One ohm is the resistance that lets 1 A flow under 1 V. Electrical work follows from it as volts times amps times seconds, so 12 V at 2 A for 60 s is 1,440 J, or 0.4 Wh.

What is Einstein’s famous formula?

Einstein’s formula is E = m × c², where c is the speed of light, 299,792,458 m/s. It gives the energy held in mass itself, in the same joules used for work. One gram of mass corresponds to 8.988 × 10¹³ J, which is far beyond any figure a push or a lift will produce.

Work Hours and Shift Lengths

Many searches for a work calculator mean time at a job, not joules. A work time calculator or hours calculator subtracts the start time from the end time. This tool does not total time cards, so the common shift lengths are listed here for anyone who arrived with that question.

To calculate work hours for any shift, write both times on a 24-hour clock and subtract. If the shift runs past midnight, add 24 hours to the end time first. Going the other way, 12 hours from 2:30 PM is 2:30 AM, and 30 minutes from 2:12 am is 2:42 am.

A work calculator with lunch takes the unpaid break off the total. A 9 to 5 shift with a 30 minute lunch is 7.5 paid hours, and an 8 hour work day with that lunch runs 8.5 hours on the clock.

For pay in hours and minutes, divide the minutes by 60 to get decimal hours. A day of 7 hours 45 minutes is 7.75 hours, and at $20 an hour the pay is $155. The same division turns a week of time-card totals into hours a payroll sheet can use.