Work and Power Calculator

Related Calculators

Work (J): Energy transferred by a force acting through displacement. It can be positive, zero, or negative depending on the force direction relative to the motion.[1]

Power (W): The rate of doing work, or work divided by time.[2]

Force magnitude (N): How strong the force is. In this calculator it is the size of the force, not a signed direction value.

Displacement (m): How far the object moves along its path for the work formula used here.

Speed (m/s): How fast the object moves along the direction of motion for the power formula used here.

Angle theta: The angle between the force direction and the motion direction. At 0 degrees the force fully helps, at 90 degrees it contributes no work, and at 180 degrees it fully opposes.

cos(theta): The along-motion factor. It tells what fraction of the force or force-times-speed points along the motion direction.

Negative result: A negative work or power value means the force removes energy from the object overall instead of adding it.[1]

Mistake: Typing a negative value for Displacement (m) or Speed (m/s) even though this calculator treats them as magnitudes.
Fix: Enter magnitudes as 0 or greater, and use Angle theta (degrees) to show whether the force helps or opposes the motion.

Mistake: Entering 90 in Angle theta (degrees) while Angle unit is set to radians.
Fix: Make Angle unit match your number. Use degrees for 90, or radians for about 1.571.

Mistake: Using minutes or hours in Time (s) without changing Time unit (selected unit) .
Fix: If you enter 2 minutes, either type 120 with seconds selected or change Time unit (selected unit) to minutes.

Mistake: Using the wrong angle meaning for Angle theta (degrees) .
Fix: Enter the angle between the force direction and the motion direction. That is the angle used in Along-motion component factor cos(theta) .

Mistake: Trying to divide by zero or a nonpositive time when solving with Time (s) .
Fix: For power from work and time, Time (s) must be greater than 0. If you are solving for time, the known power must not be 0.

Mistake: Ignoring a mismatch in Consistency check (if enough info) .
Fix: Recheck Work unit (selected unit) , Power unit (selected unit) , Time unit (selected unit) , and Angle unit before trusting the result.

• This calculator uses constant-force, straight-line formulas: work from W = F * d * cos(theta) and power from P = F * v * cos(theta) or P = W / t.
• Force magnitude (N), Displacement (m), and Speed (m/s) are treated as magnitudes, so they should be 0 or greater. Direction effects are handled by Angle theta (degrees) and its cosine.
• Time (s) must be greater than 0 when dividing by time. If time is 0, power from work and time is undefined.
• If cos(theta) is 0 or extremely close to 0, work or power from that force is 0, and solving backward for force, displacement, or speed from a nonzero result is not possible.
• Angle results found by solving backward are based on inverse cosine, so they only match situations that fit the chosen formula and valid cosine range.
• Unit conversions are handled internally in SI base units, but displayed rounding can make very tiny differences appear when you compare converted values by hand.
• The calculator shows signed results. Negative work or power is valid here and means the force is opposite the motion overall, not that the calculator failed.

Formulas used

The calculator first converts entered values to standard SI units, then applies the formula for your selected mode.

W = F * d * cos(theta)

P = W / t

P = F * v * cos(theta)

Power is work per unit time.[2] Signed results come from the cosine term: positive when the force points partly with the motion, zero at 90 degrees, and negative when the force points partly against the motion.[1]

Rearranged forms

When you choose a different unknown, the calculator rearranges the same formulas.

t = W / P

F = W / (d * cos(theta))

d = W / (F * cos(theta))

v = P / (F * cos(theta))

If the denominator is 0, such as t = 0 or cos(theta) = 0, the calculator returns an error or N/A instead of a fake answer.

Unit conversion method

The calculator stores work in joules, time in seconds, and power in watts before doing the physics. It then converts the final answer back to your chosen display unit.

1 min = 60 s

1 hr = 3600 s

1 Wh = 3600 J

1 kWh = 3,600,000 J

1 hp = 745.69987158227022 W

This keeps the math consistent when you mix units like kWh, hours, and kW.

Worked mini-example

Suppose Force magnitude (N) is 20, Displacement (m) is 10, and Angle theta (degrees) is 60. Since cos(60 degrees) = 0.5, the work is:

W = 20 * 10 * 0.5 = 100 J

If that 100 J happens in 5 s, then power is:

P = 100 / 5 = 20 W

If the angle were 180 degrees instead, the cosine would be -1, so the result would be negative. That means the force removes energy from the object overall.[1]

Consistency check

When enough values are available, the calculator compares equivalent expressions such as entered or computed power versus W / t, or power versus F * v * cos(theta). A mismatch usually means the wrong unit setting was used or the angle was not the angle between force and motion.

Assumptions behind the result

This method assumes the force and angle stay constant during the motion segment being modeled. Real situations with changing force, curved motion, friction changes, or changing speed can give different results from this simple constant-value model.[3]