Compound Lever Calculator — Mechanical Advantage

Robbie Dickson
2026-03-02T09:09:15-08:00

Free compound lever calculator. Enter effort and load arm distances for 2–5 cascaded levers to calculate total mechanical advantage and output force instantly.

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⚙ Simulator

◎ Selector

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Load Configuration

Load (W) at Lever 1100 lbs

12000 lbs

Lever 1 — First Stage

Effort Arm (L1)86.5"

1"120"

Load Arm (L2)18"

1"120"

Lever 2 — Second Stage

Effort Arm (L1)82.5"

1"120"

Load Arm (L2)9"

1"120"

Results

Compound Output Force (F₂)

--

lbs output from compound lever

Total MA

--

:1 ratio

F₁ (Lever 1 Out)

--

lbs → Lever 2

Lever 1 MA

--

:1

Lever 2 MA

--

:1

→ Find Matching Actuators

Safety Multiplier 1.5×

1.0×Suggested: 1.5×3.0×
▶ Animate Lever

💡 Engineering Insight

Adjust lever dimensions above.

Physics: rigid levers, point loads, frictionless pivots.

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Your Requirements

Force Needed25 lbs

12500 lbs

Stroke Length4"

1"60"

Min Speed0.50 in/s

0.059.00 in/s

Safety Factor

Safety Multiplier1.5×

1.0×3.0×

💡 Suggested: 1.5×
Feedback Required → Compare Top Matches
Weighted: Force 60% · Stroke 40%

Matching Actuators

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Pick up to 3 actuators.

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📹 Video Walkthrough — How to Use This Calculator

Chaining 2 lever stages in series — where the output of the first drives the input of the second — multiplies mechanical advantage far beyond what a single lever can deliver, making it possible to produce very high output forces from compact actuators without upsizing the mechanism. Use this Compound Lever Calculator to calculate total mechanical advantage and compound output force using your input load, effort arm lengths, and load arm lengths for both stages. That combination matters in industrial press design, heavy hatch mechanisms, and robotic gripper systems where peak force from a small actuator footprint is the core constraint. This page includes the full formula, a worked example, design theory, and a built-in actuator selector.

What is a Compound Lever?

A compound lever is 2 or more levers linked in series, where the output force of the first lever becomes the input load of the second. This arrangement multiplies mechanical advantage — letting a small input force produce a very large output force.

Simple Explanation

Think of it like shifting gears twice instead of once. The first lever already amplifies your push, then the second lever amplifies it again — so the final force is the product of both amplifications, not just the sum. The trade-off is travel: the more force you gain, the shorter the output movement becomes relative to the input.

Understanding Compound Levers

Overview

A compound lever links two or more levers so that the output force of one becomes the input of the next. The total mechanical advantage equals the product of each individual lever's MA, enabling very large force amplification from compact mechanisms.

How Compound Levers Multiply Force

Each lever amplifies force based on the ratio of its effort arm to its load arm. In this calculator, the effort arm (L1) is the distance from the input load (W) to the fulcrum, and the load arm (L2) is the distance from the fulcrum to the output point. The closer the output point is to the fulcrum, the greater the force amplification:

Use the formula below to calculate the output force of the first lever stage.

F₁ = W × (L1 ÷ L2)

The total compound output is:

Use the formula below to calculate the final compound output force.

F₂ = W × MA₁ × MA₂

W = input load (lbs)
MA₁ = L1a ÷ L1b (Lever 1 mechanical advantage)
MA₂ = L2a ÷ L2b (Lever 2 mechanical advantage)
F₂ = final compound output force

How to Use This Calculator

1. Set your input load (W) using the Load slider — this is the force applied at the first lever's effort end.

2. Set the Effort Arm (L1) and Load Arm (L2) lengths for both Lever 1 and Lever 2 using the sliders.

3. Adjust the Safety Multiplier to account for dynamic loading and real-world wear — 1.5× minimum is recommended.

4. Click Calculate to see your result.

Simple Example

Input load (W): 100 lbs
Lever 1 — Effort Arm: 80", Load Arm: 10" → MA₁ = 8.0
Lever 2 — Effort Arm: 60", Load Arm: 10" → MA₂ = 6.0
F₁ = 100 × 8.0 = 800 lbs
F₂ = 800 × 6.0 = 4,800 lbs compound output force — from a 100 lb input.

The Displacement Trade-Off

Force amplification comes at the cost of displacement. A system with 40:1 compound MA requires 40 times the input stroke to achieve a given output movement:

Use the formula below to calculate the required actuator input stroke.

dinput = doutput × Total MA

This is critical when sizing a linear actuator to drive the system. If you need 2 inches of output movement with a 44:1 compound lever, the actuator must provide 88 inches of stroke.

Efficiency and Friction

Each pivot point introduces friction losses. With standard bronze bushings, a single pivot operates at roughly 80–95% efficiency. Using sealed ball bearings can push each pivot above 95%, giving 90%+ system efficiency.

Common Applications

Industrial presses and clamping — Small actuators generate tonnage-level forces for stamping, forming, and assembly.

Heavy hatches and covers — Boat hatches and vault lids operated with modest actuators through compound linkages.

Brake systems — Bicycle and industrial brakes amplify hand force into high clamping pressure.

Robotic grippers — Compound lever linkages generate high grip force from compact actuators.

Platform scales — Traditional scales reduce large loads to measurable forces on the balance beam.

Design Tips

Move L2 closer to the fulcrum for more force — The smaller L2 is relative to L1, the greater the mechanical advantage. Even small changes in L2 position create large force differences.

Account for stroke multiplication — High compound MA requires proportionally longer actuator strokes.

Use bearings at all pivots — Friction losses multiply in a compound system. Sealed bearings can reduce required input by 10–15%.

Make the linkage rigid — The connection between levers must withstand intermediate forces without deflection.

Apply a safety factor of 1.5× minimum — Dynamic loading and wear increase real-world requirements.

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