Work Calculator

Online Work Calculator

Use this online work calculator to determine the total amount of work done on an object. You can also calculate related quantities such as power, force, and displacement using different units. Below, we explain the work equation in physics along with examples for better understanding.

What is Work in Physics?

Work (W) is defined as the product of the force (F) applied to an object and the displacement (d) of that object. In other words, work represents the energy transferred to or from an object via a force along a displacement.

SI Unit of Work: Joule (J), where 1 joule = 1 newton-meter (N·m). The SI unit can also be expressed as kg·m²/s².

Work Formula:

W = F × d

W = work done
F = force applied
d = displacement of the object

Rearranged Formulas:

Force: F = W / d
Displacement: d = W / F

Work from Change in Velocity

When an object changes speed from initial velocity v₀ to final velocity v₁ over time t, force and distance can be expressed as:

F = m × a = m × (v₁ - v₀) / t

d = t × (v₀ + v₁) / 2

Combining these into the work formula:

W = F × d = [m × (v₁ - v₀)/t] × [t × (v₀ + v₁)/2] = (m / 2) × (v₁² - v₀²)

The work calculator can compute work directly using this formula. You can also use an Online Velocity Calculator to find velocities if needed.

Types of Work

Positive (+) work: Force and displacement in the same direction (0° ≤ θ < 90°). Example: pushing a door forward.
Zero (0) work: Force and displacement are perpendicular (θ = 90°). Example: carrying a jug of water while walking horizontally.
Negative (-) work: Force and displacement in opposite directions (90° < θ ≤ 180°). Example: lifting a football against gravity.

How to Calculate Work Done

Steps to calculate work manually:

Find the force using F = m × a.
Measure the angle between force and displacement.
Substitute all values into the work formula: W = F × d × cos(θ).

Example:

Given:

Force = 15 N
Angle = 45°
Displacement = 22 m

Solution:

Component of force along displacement: F = 15 × cos 45° ≈ 10.60 N

Work done: W = 10.60 × 22 ≈ 233 J

You can also use an Online Displacement Calculator for calculating displacement using acceleration, velocity, and time.

Power (P)

Power represents the rate at which work is done. SI unit: Watt (W), equal to one joule per second.

P = W / t

P = power
W = work done
t = time taken

Using the Work Calculator

Input:

Select "Work" or "Power" from the menu.
If "Work," choose between Force & Displacement or Change in Velocity.
Enter the required values with units.
Click "Calculate."

Output:

The calculator provides the value with correct SI units.
Displays the formula and step-by-step solution.

FAQs

What is the relationship between torque and rotation?

Torque changes angular velocity and angular momentum. By applying torque, angular momentum is transformed, which directly relates these quantities.

What is the relationship between work and energy?

Work is the energy transferred to move an object. Hence, work and energy are directly related.

Conclusion

An online work calculator simplifies the calculation of work, power, force, and displacement. It ensures accurate results in SI units without time-consuming manual calculations.

References

Wikipedia: Work and Energy
Britannica: Work by Gravity
Physics Info: Work-Energy Theorem