⚖️ Fulcrum Calculator
Calculate forces and distances on a lever
Input force applied on one side of the fulcrum
Distance from Force 1 to fulcrum
Distance from fulcrum to Force 2 (output)
How to Use This Calculator
Enter Force 1
Input the known force applied on one side of the fulcrum. This is the input force. Use consistent units (Newtons for metric, pounds for imperial) throughout the calculation.
Enter Distance 1
Enter the distance from Force 1 to the fulcrum (pivot point). This is the lever arm length on the input side. Use the same units (meters or feet) as Distance 2.
Enter Distance 2
Input the distance from the fulcrum to where Force 2 will be applied (output side). This is the lever arm length on the output side. Use the same units as Distance 1.
Calculate Force 2
Click "Calculate Force 2" to determine the output force required to balance the lever. The calculator uses the principle of moments (F₁ × d₁ = F₂ × d₂) to find the unknown force.
Formula
F₁ × d₁ = F₂ × d₂
F₂ = (F₁ × d₁) / d₂
Where:
- F₁ = Input Force (known force on one side)
- F₂ = Output Force (force to balance, calculated)
- d₁ = Distance from Force 1 to fulcrum
- d₂ = Distance from fulcrum to Force 2
Example Calculation:
For Force 1 = 100 N, Distance 1 = 2 m, Distance 2 = 1 m:
F₂ = (100 × 2) / 1
F₂ = 200 / 1
F₂ = 200 N
This means a 200 N force at 1 m balances a 100 N force at 2 m.
Another example: 50 lbs at 3 ft, Distance 2 = 1.5 ft:
F₂ = (50 × 3) / 1.5 = 100 lbs
Note: This formula is based on the principle of moments (torque balance) for a lever in equilibrium. When the lever is balanced, the clockwise moments equal the counterclockwise moments. This is also known as the law of the lever, discovered by Archimedes.
About Fulcrum Calculator
The Fulcrum Calculator determines the force required to balance a lever system using the principle of moments. A fulcrum is the pivot point of a lever, and when balanced, the product of force and distance on one side equals the product of force and distance on the other side. This fundamental principle explains how levers multiply force or distance, making it essential for understanding mechanical advantage, tool design, and physics applications.
When to Use This Calculator
- Physics Problems: Solve lever and torque problems in physics homework and exams
- Mechanical Design: Design levers, seesaws, or balance systems
- Tool Selection: Understand how crowbars, pry bars, and other tools multiply force
- Educational Purposes: Learn about mechanical advantage and simple machines
- Engineering Calculations: Calculate forces in mechanical systems and structures
Why Use Our Calculator?
- ✅ Principle of Moments: Uses the fundamental lever balance equation
- ✅ Simple Input: Just enter force and distances
- ✅ Flexible Units: Works with any consistent unit system
- ✅ Step-by-Step Display: Shows the complete calculation process
- ✅ Free Tool: No registration required, works on all devices
Understanding Fulcrums and Levers
A fulcrum is the pivot point around which a lever rotates. The principle of moments states that for a lever in equilibrium, the sum of clockwise moments equals the sum of counterclockwise moments. This means F₁ × d₁ = F₂ × d₂. When d₂ is smaller than d₁, F₂ must be larger than F₁ to maintain balance, creating mechanical advantage. This is why a crowbar can lift heavy objects - the long handle (d₁) allows a small input force to create a large output force over a short distance (d₂).
Common Applications
Simple Machines: Levers are one of the six simple machines. Seesaws, crowbars, bottle openers, and wheelbarrows all use the fulcrum principle to multiply force or change the direction of applied force.
Engineering: Mechanical engineers use fulcrum calculations to design machines, lifting equipment, and mechanical systems that require force multiplication or precise balance.
Everyday Tools: Many hand tools use levers - scissors, pliers, nutcrackers, and wrenches all apply the fulcrum principle to make tasks easier.
Tips for Best Results
- Use consistent units throughout - don't mix metric (N, m) with imperial (lbs, ft)
- Measure distances from the fulcrum (pivot point) to the point where force is applied
- For levers with multiple forces, calculate moments separately and sum them
- Remember that mechanical advantage = d₁ / d₂ when calculating force multiplication
- If Force 2 is larger than Force 1, Distance 2 must be smaller than Distance 1
Frequently Asked Questions
What is a fulcrum?
A fulcrum is the pivot point or support on which a lever rotates or balances. It's the fixed point around which the lever moves. In a seesaw, the fulcrum is the center support. In a crowbar, the fulcrum is where the bar contacts the surface you're prying against. The position of the fulcrum determines the mechanical advantage of the lever.
How does distance from the fulcrum affect force?
The farther from the fulcrum a force is applied, the less force is needed to create the same moment (torque). This is why longer levers provide more mechanical advantage. For example, applying force at twice the distance requires half the force to balance the same load. This relationship is linear: if you double the distance, you halve the required force.
What is mechanical advantage in a lever?
Mechanical advantage (MA) is the ratio of output force to input force, or equivalently, the ratio of input distance to output distance (MA = d₁ / d₂). When MA is greater than 1, the lever multiplies force but reduces distance. When MA is less than 1, the lever multiplies distance but requires more force. Mechanical advantage allows us to lift heavy objects with less effort.
Can I use this for a lever with the fulcrum at the end?
Yes, this calculator works for any lever configuration. Just enter the distances from the fulcrum to each force. For example, in a wheelbarrow, the fulcrum is at the wheel (one end), and you apply force at the handles while the load is in the middle. Measure distances from the wheel to the handles and from the wheel to the load's center of gravity.
What if my lever isn't balanced?
If the lever isn't balanced, there will be a net torque causing rotation. To calculate the net torque, find F₁ × d₁ and F₂ × d₂, then subtract them. If the result is positive, the lever rotates in one direction; if negative, it rotates in the opposite direction. This calculator assumes equilibrium (balanced lever), so it calculates the force needed for balance.