Effort F₁
Fulcrum
Load F₂
N
Enter a valid load force.
Weight or resistance being overcome
m
Enter a valid load arm distance.
Distance from fulcrum to load
m
Enter a valid effort arm distance.
Distance from fulcrum to where you push
💡 F₁ × d₁ = F₂ × d₂
Effort = (Load × Load arm) ÷ Effort arm
Longer effort arm → less force needed.
Effort = (Load × Load arm) ÷ Effort arm
Longer effort arm → less force needed.
N
Enter a valid effort force.
m
Enter a valid effort arm.
m
Enter a valid load arm.
💡 Load = (Effort × Effort arm) ÷ Load arm
MA = Effort arm ÷ Load arm
MA = Effort arm ÷ Load arm
N
Enter a valid effort force.
N
Enter a valid load force.
m
Enter a valid lever length.
Total length from effort end to load end
💡 Fulcrum from effort end:
d₁ = (F₂ × L) ÷ (F₁ + F₂)
d₁ = (F₂ × L) ÷ (F₁ + F₂)
Result
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Sources & Methodology
Lever equations verified against Archimedes’ principle of moments and standard mechanics textbooks.
Physics Classroom — Principles of Simple Machines
Reference for lever class definitions, mechanical advantage, and the principle of moments as applied to real-world machines.
Khan Academy — Torque & Levers
Derivation of F₁d₁ = F₂d₂ from torque principles; worked examples of all three lever classes.
Principle of moments: F₁ × d₁ = F₂ × d₂
Find effort: F₁ = (F₂ × d₂) / d₁
Find load: F₂ = (F₁ × d₁) / d₂
Find fulcrum (from effort end): d₁ = (F₂ × L) / (F₁ + F₂); d₂ = L − d₁
Mechanical advantage: MA = F₂/F₁ = d₁/d₂
Torque: τ = F × d (Newton-metres, Nm)
Find effort: F₁ = (F₂ × d₂) / d₁
Find load: F₂ = (F₁ × d₁) / d₂
Find fulcrum (from effort end): d₁ = (F₂ × L) / (F₁ + F₂); d₂ = L − d₁
Mechanical advantage: MA = F₂/F₁ = d₁/d₂
Torque: τ = F × d (Newton-metres, Nm)
⏱ Last reviewed: April 2026
How to Use the Fulcrum Calculator in 2026
A fulcrum is the pivot point of a lever — the fixed support around which the lever rotates when forces are applied on either side. The position of the fulcrum relative to the effort force and the load determines the mechanical advantage of the system. This calculator solves the principle of moments in three directions: find the effort needed, the load achievable, or where the fulcrum must sit.
The Lever Balance Equation
F₁ × d₁ = F₂ × d₂
F₁ = effort force (N) d₁ = effort arm (m)
F₂ = load force (N) d₂ = load arm (m)
Example — crowbar lifting 500 N:
Load arm d₂ = 0.05 m | Effort arm d₁ = 1.0 m
F₁ = (500 × 0.05) / 1.0 = 25 N MA = 500/25 = 20×
F₂ = load force (N) d₂ = load arm (m)
Example — crowbar lifting 500 N:
Load arm d₂ = 0.05 m | Effort arm d₁ = 1.0 m
F₁ = (500 × 0.05) / 1.0 = 25 N MA = 500/25 = 20×
The Three Lever Classes
| Class | Arrangement | Mechanical Advantage | Real Examples |
|---|---|---|---|
| Class 1 | Effort — Fulcrum — Load | Can be >1 or <1 | Seesaw, crowbar, scissors |
| Class 2 | Fulcrum — Load — Effort | Always >1 | Wheelbarrow, nutcracker |
| Class 3 | Fulcrum — Effort — Load | Always <1 | Tweezers, forearm, fishing rod |
Practical Applications
- Crowbar: A 1.2 m bar with fulcrum 0.05 m from load gives MA = 24 — 100 N lifts 2,400 N
- Seesaw balance: Find where a 30 kg child must sit to balance a 75 kg adult at 1.5 m from centre
- Engineering design: Determine optimal fulcrum position for brake pedals, control linkages, and scissor lifts
- Medical devices: Forceps, surgical scissors, and retractors all use class 1 or 3 lever principles
💡 Archimedes stated: “Give me a long enough lever and a place to stand, and I shall move the Earth.” This expresses the power of the lever — with sufficient effort arm length, any load can theoretically be overcome. In practice, material strength and deflection set the real limits.
Frequently Asked Questions
A fulcrum is the fixed pivot point of a lever. It is the point around which the lever rotates when forces are applied. Its position relative to effort and load determines the mechanical advantage — closer to the load means more force multiplication; closer to the effort means more speed and range.
F1 x d1 = F2 x d2 (the principle of moments). F1 is effort force, d1 is effort arm, F2 is load force, d2 is load arm. The lever balances when clockwise torque equals anti-clockwise torque about the fulcrum. This equation holds for all three lever classes.
Effort F1 = (F2 x d2) / d1. For a 500 N load 0.3 m from the fulcrum, with a 1.5 m effort arm: F1 = (500 x 0.3) / 1.5 = 100 N. Mechanical advantage = 500/100 = 5 — you multiply your applied force 5 times.
Mechanical advantage MA = Load / Effort = Effort arm / Load arm. MA greater than 1 means force multiplication — you exert less force than the output. MA less than 1 (Class 3 levers) means you exert more force but gain speed, range of motion, or precision at the output end.
Class 1: fulcrum between effort and load — seesaw, crowbar, scissors. MA can be above or below 1. Class 2: load between fulcrum and effort — wheelbarrow, nutcracker, bottle opener. MA always above 1. Class 3: effort between fulcrum and load — tweezers, forearm, fishing rod. MA always below 1 but provides increased speed and reach.
For a lever of total length L with effort F1 and load F2 at opposite ends: fulcrum distance from effort end = (F2 x L) / (F1 + F2). For 100 N effort and 300 N load on a 2 m lever: d1 = (300 x 2) / 400 = 1.5 m from effort, 0.5 m from load. MA = 300/100 = 3.
Mass1 x distance1 = mass2 x distance2 (weight = mg cancels when g is the same). If a 60 kg adult sits 1.5 m from the centre, a 40 kg child must sit at 60 x 1.5 / 40 = 2.25 m from the centre. The heavier person always sits closer to the fulcrum to balance.
Torque = Force x perpendicular distance from pivot (Newton-metres). The lever balances when torques are equal: F1 x d1 = F2 x d2. A 100 N force at 1.5 m creates 150 Nm of torque about the fulcrum. This must be matched by the load torque for equilibrium.
Archimedes demonstrated that effort x effort arm = load x load arm. Increasing the effort arm reduces the required force proportionally. His statement that a long enough lever could move the Earth illustrates that with sufficient arm ratio, any load is theoretically overcome — limited only by material strength.
Class 1: seesaw, crowbar, scissors, pliers, balance scale. Class 2: wheelbarrow (load between wheel-fulcrum and handles-effort), nutcracker, bottle opener, door with hinge at one end. Class 3: tweezers, forearm lifting a load, fishing rod, broom, stapler. Each trades off force against speed and range.
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