Work Calculator

by
Work Calculator (Physics)
Work (W)Force (F)Distance / Displacement (d)Angle (θ)
J
N
m
°
Answer:
Enter values and click Calculate.
function updateFields(){var solveFor=document.getElementById('solve_for').value;document.getElementById('row_w').style.display=(solveFor==='work')?'none':'table-row';document.getElementById('row_f').style.display=(solveFor==='force')?'none':'table-row';document.getElementById('row_d').style.display=(solveFor==='distance')?'none':'table-row';document.getElementById('row_a').style.display=(solveFor==='angle')?'none':'table-row';document.getElementById('answer').innerHTML='Enter values and click Calculate.';}function calculateResult(){var type=document.getElementById('solve_for').value;var w=parseFloat(document.getElementById('val_w').value);var f=parseFloat(document.getElementById('val_f').value);var d=parseFloat(document.getElementById('val_d').value);var a=parseFloat(document.getElementById('val_a').value);var showSteps=document.getElementById('steps').checked;var ansDiv=document.getElementById('answer');var res=0;var details="";if(type==='work'){if(isNaN(f)||isNaN(d)||isNaN(a)){alert('Please enter Force, Distance, and Angle');return;}var rad=a*(Math.PI/180);res=f*d*Math.cos(rad);details="Work (W) = F × d × cos(θ)
W = "+f+" × "+d+" × cos("+a+"°)
W = "+res.toFixed(4)+" Joules (J)";ansDiv.innerHTML="Work (W) = "+res.toFixed(4)+" J"+(showSteps?"
"+details+"
":"");}else if(type==='force'){if(isNaN(w)||isNaN(d)||isNaN(a)){alert('Please enter Work, Distance, and Angle');return;}var rad=a*(Math.PI/180);var cosA=Math.cos(rad);if(Math.abs(cosA)<0.00001){ansDiv.innerHTML="Error: Force cannot be determined when angle is 90° (cos(90)=0).";return;}res=w/(d*cosA);details="Force (F) = W / (d × cos(θ))
F = "+w+" / ("+d+" × cos("+a+"°))
F = "+res.toFixed(4)+" Newtons (N)";ansDiv.innerHTML="Force (F) = "+res.toFixed(4)+" N"+(showSteps?"
"+details+"
":"");}else if(type==='distance'){if(isNaN(w)||isNaN(f)||isNaN(a)){alert('Please enter Work, Force, and Angle');return;}var rad=a*(Math.PI/180);var cosA=Math.cos(rad);if(Math.abs(cosA)<0.00001){ansDiv.innerHTML="Error: Distance cannot be determined when angle is 90°.";return;}res=w/(f*cosA);details="Distance (d) = W / (F × cos(θ))
d = "+w+" / ("+f+" × cos("+a+"°))
d = "+res.toFixed(4)+" Meters (m)";ansDiv.innerHTML="Distance (d) = "+res.toFixed(4)+" m"+(showSteps?"
"+details+"
":"");}else if(type==='angle'){if(isNaN(w)||isNaN(f)||isNaN(d)){alert('Please enter Work, Force, and Distance');return;}var cosA=w/(f*d);if(cosA>1||cosA<-1){ansDiv.innerHTML="Error: Invalid parameters. cos(θ) must be between -1 and 1.";return;}res=Math.acos(cosA)*(180/Math.PI);details="cos(θ) = W / (F × d)
cos(θ) = "+w+" / ("+f+" × "+d+")
θ = arccos("+cosA.toFixed(4)+")
θ = "+res.toFixed(2)+"°";ansDiv.innerHTML="Angle (θ) = "+res.toFixed(2)+"°"+(showSteps?"
"+details+"
":"");}}updateFields();

Calculator Use

This work calculator is a specialized tool designed to solve physics problems involving mechanical work. In physics, "work" is defined as the measure of energy transfer that occurs when an object is moved over a distance by an external force at least part of which is applied in the direction of the displacement.

By using this tool, you can quickly find any of the four variables in the standard work formula: Work ($W$), Force ($F$), Distance or Displacement ($d$), or the Angle ($\theta$) between the force and the direction of motion. This is particularly useful for students, engineers, and physics enthusiasts who need accurate results without manual trigonometric calculations.

Work (W)
The amount of energy transferred by the force, typically measured in Joules (J) or Newton-meters (N·m).
Force (F)
The magnitude of the constant force applied to the object, measured in Newtons (N).
Distance (d)
The displacement of the object during the application of force, measured in meters (m).
Angle (θ)
The angle (in degrees) between the force vector and the displacement vector. If the force is applied in the exact same direction as the motion, the angle is 0°.

How It Works

The work calculator utilizes the fundamental mechanical work equation. To calculate work, we must account for the component of the force that acts in the direction of the movement. This is why the cosine of the angle is required.

W = F × d × cos(θ)

Depending on which variable you are trying to find, the formula is rearranged as follows:

  • To find Force: $F = W / (d \times \cos(\theta))$
  • To find Distance: $d = W / (F \times \cos(\theta))$
  • To find Angle: $\theta = \arccos(W / (F \times d))$

Calculation Example

Example Scenario: A person pulls a heavy crate across a floor with a force of 50 Newtons. The rope is held at an angle of 30 degrees to the horizontal floor. The crate is moved 10 meters. How much work is done?

Step-by-step solution:

  1. Identify the values: Force ($F$) = 50 N, Distance ($d$) = 10 m, Angle ($\theta$) = 30°.
  2. Apply the formula: $W = F \times d \times \cos(\theta)$
  3. Substitute the values: $W = 50 \times 10 \times \cos(30°)$
  4. Calculate the cosine: $\cos(30°) \approx 0.866$
  5. Calculate the result: $W = 500 \times 0.866 = 433.01$
  6. Result: Total Work = 433.01 Joules

Common Questions

What is a Joule?

A Joule (J) is the standard unit of energy and work in the International System of Units (SI). One Joule is equal to the work done when a force of one Newton moves an object a distance of one meter in the direction of the force.

What happens if the angle is 90 degrees?

If the angle is 90 degrees ($\cos(90°) = 0$), the work done is zero. This occurs because the force is perpendicular to the motion, meaning no component of that force is contributing to the displacement. An example is carrying a bucket while walking horizontally; your upward force doesn't do "work" on the bucket in the direction you are walking.

Can work be negative?

Yes, work is negative when the force applied is in the opposite direction of the displacement (angle between 90° and 180°). For example, the force of friction does negative work on a sliding object because it acts against the direction of motion, removing kinetic energy from the system.

Why use a work calculator?

Using a work calculator ensures precision, especially when dealing with non-integer angles or very large force values. It helps avoid common errors like using Sine instead of Cosine or forgetting to convert degrees to radians during manual calculation.

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