Gear Ratio Calculator

This Gear Ratio Calculator is an advanced tool able to calculate up to four levels and even the ratios of planetary gear systems, using the Willis Equation. We’ve provided complete instructions below the calculator to help you use the calculator.

If you still find it difficult or confusing using the calculator, please contact us and one of our experts will help. We also have an article on How Gear Reducers Work.

What Are Gears and Why Do They Matter?

Think of gears like the wheels on a bicycle. When you pedal, you’re turning one gear (connected to the pedals) which turns a chain that spins another gear (connected to the back wheel). Depending on the size difference between these gears, you can either:

• Go faster with less power (like riding downhill)
• Go slower but with more power (like climbing a steep hill)

This same principle applies to machines, cars, robots, and countless other devices that need to convert speed and power.

What This Calculator Does

This calculator helps you figure out:

1. How much slower or faster your output will be compared to your input
2. How much more or less force you’ll have at the output
3. How efficient your gear system will be (how much energy gets “lost” to friction)

Basic Setup – Getting Started

Step 1: Choose Your Number of Stages

• 1 Stage: One pair of gears (simplest)
• 2-4 Stages: Multiple gear pairs working together (more complex, but can achieve bigger speed/force changes)

Start with 1 stage if you’re new to this.

Step 2: Choose Your Input Method

You have two ways to describe your gears:

Option A: Teeth (Recommended for beginners)

• Count the number of “teeth” (the pointy bits) on each gear
• Example: A small gear might have 20 teeth, a large gear might have 60 teeth

Option B: Pitch Diameter

• Measure the diameter of the gear (more advanced)
• Use this if you have engineering drawings or precise measurements

Step 3: Choose Your Measurement System

• Imperial: Uses inches and “Diametral Pitch” (common in the US)
• Metric: Uses millimeters and “Module” (common elsewhere)

If you’re just learning, the system choice won’t affect your basic understanding.

Understanding Your Gears

Driver vs. Driven Gear

• Driver Gear: The one being turned by your motor/engine (the input)
• Driven Gear: The one being turned by the driver gear (the output)

The Golden Rule of Gears

• Small driver + Large driven = SLOWER output with MORE force
• Large driver + Small driven = FASTER output with LESS force

Real-World Examples

1. Car in first gear: Small gear drives large gear → slow but powerful (for hills)
2. Car in high gear: Large gear drives small gear → fast but less powerful (for highway)
3. Drill press: Multiple stages to get very slow, very powerful drilling

Filling Out the Calculator

Basic Information (Required)

1. Driver: Enter the tooth count (or diameter) of your input gear
2. Driven: Enter the tooth count (or diameter) of your output gear

Example: Driver = 20 teeth, Driven = 60 teeth

Optional but Useful Information

Gear Type: Choose what kind of gears you’re using

• Auto: Let the calculator guess (fine for beginners)
• Spur/Helical: Standard straight or angled teeth (most common)
• Bevel: Gears that change direction (like in a car’s differential)
• Planetary: Complex systems with multiple gears (automatic transmissions)
• Worm: Screw-like gear (very high reduction but less efficient)

Input RPM: How fast is your motor spinning?

• RPM = Revolutions Per Minute
• Example: A typical electric motor might spin at 1750 RPM

Input Torque: How much rotational force does your motor produce?

• Torque is like “rotational strength”
• Check your motor’s specifications for this number

Reading Your Results

Overall Ratio

This tells you the speed relationship between input and output.

• Ratio of 3:1: Output spins 3 times slower than input (reduction)
• Ratio of 0.5:1: Output spins 2 times faster than input (overdrive)

Overall Efficiency

This tells you how much energy is lost to friction.

• 0.95 (95%): Very good – only 5% energy lost
• 0.80 (80%): Okay – 20% energy lost
• 0.60 (60%): Poor – 40% energy lost

Output RPM

If you entered an input RPM, this shows how fast your output will spin.

Output Torque

If you entered input torque, this shows how much rotational force you’ll have at the output.

Practical Examples

Example 1: Simple Speed Reduction

• Goal: Slow down a 1750 RPM motor to about 350 RPM
• Setup:
  • Driver gear: 20 teeth
  • Driven gear: 100 teeth
  • Ratio: 100 ÷ 20 = 5:1
• Result: 1750 ÷ 5 = 350 RPM output

Example 2: Increasing Torque

• Goal: Increase torque from 5 lb⋅ft to about 20 lb⋅ft
• Setup: Same as above (5:1 reduction)
• Result: 5 × 5 × 0.98 (efficiency) = 24.5 lb⋅ft output

Example 3: Multi-Stage for High Reduction

• Goal: Reduce 1750 RPM to 17.5 RPM (100:1 reduction)
• Setup: Two stages of 10:1 each
  • Stage 1: 10 teeth driver, 100 teeth driven (10:1)
  • Stage 2: 10 teeth driver, 100 teeth driven (10:1)
  • Total: 10 × 10 = 100:1 reduction
• Result: 1750 ÷ 100 = 17.5 RPM

Tips for Beginners

1. Start Simple: Use 1 stage with round numbers (like 20 and 60 teeth)
2. Think Backwards: Know your desired output speed/torque first, then work backwards
3. Check Your Math: Larger driven gear = slower output but more torque
4. Consider Efficiency: Worm gears give huge reductions but waste more energy
5. Use the Export Features: Save your calculations for future reference

Common Mistakes to Avoid

• Confusing driver and driven: Remember, driver is input, driven is output
• Ignoring efficiency: Real gears aren’t 100% efficient
• Forgetting about space: Bigger gears need more room
• Over-complicating: Start with simple gear ratios before trying complex multi-stage systems

Advanced Features (When You’re Ready)

• Center Distance: How far apart your gear centers need to be
• CSV Export: Save data to analyze in spreadsheets
• PDF Export: Create professional reports
• Unit Conversions: Switch between different torque measurements

Getting Help

If you’re designing something specific:

1. Start with your desired output (speed and torque)
2. Work backwards to find the right gear ratios
3. Use this calculator to verify your math
4. Consider consulting with a mechanical engineer for critical applications

Remember: This calculator is a powerful tool, but gear selection also depends on factors like load, durability, noise, and cost that aren’t included in these calculations.

If you want the experts to run the numbers and look at your gears, Contact Us!