Calculate constant-force work from force, displacement and angle, or solve for force or displacement, with metric and imperial unit conversions.

Calculate work done by the specified force.

Constant force and straight displacement. Force and distance are magnitudes; the angle sets the work sign. The default 0ยฐ assumes parallel force and motion.

Forceโ€“displacement angle

Energy from Force Formula

The following equation gives the work done by a constant force over a straight displacement. Work may be positive, negative or zero.

E = F ร— d ร— cos(ฮธ)
  • Where E is the work done (energy transferred) (joules)
  • F is the applied force magnitude (N)
  • d is the displacement magnitude (m)
  • ฮธ is the angle between the force and the displacement

To calculate energy (work) from a force, multiply the force by the displacement and by cos(ฮธ). When the force is along the direction of motion, ฮธ = 0ยฐ and the formula simplifies to E = Fยทd. At 90ยฐ, that force does no work; beyond 90ยฐ it does negative work. Work by the net force equals the change in kinetic energy; the work of one applied force need not equal the total energy change. The inverse solvers require a nonzero denominator and a work sign consistent with the angle.

Footโ€‘pound force to Joules Conversion Table (1 ftยทlbf = 1.35582 J)
Footโ€‘pound force (ftยทlbf) Joules (J)
0.250.339
0.50.678
11.356
22.712
56.779
1013.558
1520.337
2027.116
2533.895
3040.675
4054.233
5067.791
75101.686
100135.582
150203.373
200271.164
250338.954
300406.745
500677.909
10001355.818
Conversions use 1 ftยทlbf = 1.3558179483314 J exactly; table values are rounded. Inverse: 1 J โ‰ˆ 0.737562 ftยทlbf.

How to Calculate Energy from Force?

The following example problems outline the steps and information needed to calculate the Energy from Force.

Example Problem #1

  1. First, determine the total force (N). In this example, the total force is 4 N.
  2. Next, determine the distance (m). For this problem, the distance is 8 m.
  3. Next, determine the angle between the force and displacement. In this case, the force is along the direction of motion, so ฮธ = 0ยฐ.
  4. Finally, calculate the Energy from Force using the formula above.

E = F*d*cos(ฮธ)

Inserting the values from above and solving the equation yields: 

E = 4*8*cos(0ยฐ) = 32 (joules)

Example Problem #2

Using the same method as above, first, we need to measure or determine the variables required by the equation. For this example problem, these are provided as follows: 

total force (N) = 9

distance (m) = 4

angle (ฮธ) = 0ยฐ

Entering these given values into the calculator or the formula above yields: 

E = 9*4*cos(0ยฐ) = 36 (joules)