Gear Ratio Calculator
This gear ratio calculator shows you exactly how your gears will perform before you build anything. Plug in your teeth counts and motor RPM, and you'll see the output speed and ratio instantly.
Whether you're troubleshooting a 3D printer that's skipping steps, sizing gears for a robotics project, or just trying to understand why your electric scooter can't make it up that one hill on your commute—this tool takes the guesswork out of gear selection.
What is Gear Ratio?
Gear ratio is simply how many times your input gear needs to spin to rotate the output gear once.
The math is straightforward: count the teeth on both gears, then divide.
Gear Ratio = Output Gear Teeth ÷ Input Gear Teeth
Say your motor drives a 20-tooth gear that meshes with an 80-tooth gear. That's 80 ÷ 20 = 4:1. Your motor spins four times for every single turn of the output shaft.
You'll see this written a few different ways—4:1, 4.0, or 4/1. They all mean the same thing: the output turns at one-quarter the input speed.
Here's what trips people up: a "bigger" ratio like 10:1 doesn't mean faster. It means slower output with more torque. The first number tells you how much you're trading speed for power.
The Speed-Torque Tradeoff (This is the Important Part)
Every gear system makes a trade. More torque means less speed. More speed means less torque. You can't cheat physics on this one.
A 4:1 ratio cuts your output speed to one-quarter of the input—but your output torque jumps to roughly four times the input. This is why first gear in your car feels punchy but tops out at 30 mph, while fifth gear cruises effortlessly but can't climb a steep driveway from a stop.
Gear Ratio | What Happens to Speed | What Happens to Torque | Good For |
|---|---|---|---|
1:1 | Stays the same | Stays the same | Direct drive, max speed |
2:1 | Cut in half | Doubled | Light reduction |
4:1 | Cut to 25% | Quadrupled | Most hobby projects |
10:1 | Cut to 10% | 10× stronger | Heavy lifting, precision |
Bottom line: If your project stalls, struggles, or skips—you probably need a higher ratio. If it's sluggish and your motor has power to spare—go lower.
How to Use This Calculator
1. Enter your gear teeth counts Put in the tooth count for your driving gear (the one connected to your motor) and your driven gear (the one connected to whatever you're trying to move). Most gears have the count stamped on them. If not, you're counting by hand—I've been there.
2. Add your motor's RPM This is the rotational speed of your input shaft. Check your motor's datasheet for the rated speed or no-load speed. Stepper motors often list this as steps per second, which you'll need to convert.
3. Check your results You'll get the gear ratio and output RPM. Compare these against what your project actually needs. If the numbers don't work, adjust your gear sizes and recalculate—much easier than rebuilding after the fact.
The Formulas (For Reference)
You don't need to memorize these—that's what the calculator is for—but here's what's happening behind the scenes:
Gear Ratio:
Ratio = Driven Teeth ÷ Driving Teeth
Output Speed:
Output RPM = Input RPM ÷ Ratio
Output Torque (theoretical):
Output Torque = Input Torque × Ratio
Quick worked example:
- Motor gear: 20 teeth at 1,000 RPM with 0.5 Nm torque
- Output gear: 80 teeth
The math:
- Ratio = 80 ÷ 20 = 4:1
- Output speed = 1,000 ÷ 4 = 250 RPM
- Output torque = 0.5 × 4 = 2.0 Nm
One thing the formula doesn't tell you: friction eats about 5-15% of that torque in a real system. Budget for 90% efficiency on a well-lubricated spur gear setup, less if things are dry or misaligned.
Common Ratios by Application
I've found these ranges work as solid starting points, though your specific setup might need adjustment:
Application | Typical Ratio | Why It Works |
|---|---|---|
Why It Works | 3:1 to 5:1 | Enough torque for smooth bed movement without killing print speed |
Electric bike hub | 3:1 to 5:1 | Handles hills without capping your flat-ground speed |
Robotics arm | 5:1 to 50:1 | Servos need serious mechanical advantage to lift anything |
Conveyor belt | 10:1 to 30:1 | Slow and steady wins here—speed doesn't matter, pulling force does |
Electric scooter | 4:1 to 6:1 | The eternal compromise between acceleration and top speed |
CNC spindle | 1:1 to 3:1 | You need those RPMs for cutting—don't gear them away |
Winch or hoist | 20:1 to 100:1 | Pure torque multiplication, nobody cares how fast the cable reels |
How to Pick the Right Ratio
It comes down to one question: does your system need more speed or more force?
Go higher (5:1, 10:1, or more) when:
- Your motor has speed but not muscle
- Things stall under load
- You need precise, controlled movement
- You're lifting, pushing, or gripping something heavy
Go lower (2:1, 3:1) when:
- Speed matters more than force
- Your motor already has adequate torque
- You're fighting size or weight constraints
- The system works fine, just slowly
My approach: Start with your desired output speed, calculate backward to find the ratio, then sanity-check that your motor can actually deliver enough torque at that ratio. If it can't, bump up the ratio or find a beefier motor.
Real Examples with Actual Numbers
3D Printer Z-Axis
I sized this for a bed-slinger style printer where the bed moves up and down.
- Motor: NEMA 17 stepper at 200 RPM
- Motor gear: 20 teeth
- Lead screw gear: 80 teeth
Results:
- Ratio: 80 ÷ 20 = 4:1
- Lead screw speed: 200 ÷ 4 = 50 RPM
- Torque: 4× the stepper's native output
This setup eliminated the Z-banding I was getting with a direct-drive configuration. The stepper had enough mechanical advantage to move the bed smoothly without microstepping errors showing up as layer artifacts.
Electric Scooter That Couldn't Climb
A friend asked me to look at his scooter that would bog down on even gentle inclines.
- Motor: 500W brushless at 3,000 RPM
- Original sprocket: 13T motor, 44T wheel (3.4:1)
- Wheel: 8-inch diameter
Original top speed: ~21 mph (great on flats, useless on hills)
The fix: Swapped to an 11T motor sprocket.
- New ratio: 44 ÷ 11 = 4:1
- New wheel speed: 3,000 ÷ 4 = 750 RPM
- New top speed: ~18 mph
He lost 3 mph on the top end but gained enough torque to handle his commute without getting off and walking. Worth the trade.
Robotics Gripper
Hobby servos have almost no torque. Gearing fixes that.
- Servo: SG90, 60 RPM, 0.18 Nm (pathetic for gripping)
- Pinion: 12 teeth
- Driven gear: 48 teeth
Results:
- Ratio: 48 ÷ 12 = 4:1
- Gripper close speed: 60 ÷ 4 = 15 RPM (still plenty fast)
- Grip torque: 0.18 × 4 × 0.9 = ~0.65 Nm actual
The gripper went from dropping parts to holding them securely. A $3 servo doing the job of a $15 one, just with some plastic gears in between.
Conveyor for a Workshop
Needed to move small parts bins along a workbench.
- Motor: Standard 1,750 RPM induction motor
- Drive gear: 15 teeth
- Driven gear: 45 teeth
Results:
- Ratio: 45 ÷ 15 = 3:1
- Belt drive speed: 1,750 ÷ 3 = 583 RPM
- Torque: 3× motor output
Smooth, consistent movement with plenty of force to handle loaded bins. A higher ratio would work too, but there was no need—the motor wasn't straining.
A Note on Real-World Results
These calculations assume perfect conditions—ideal meshing, no friction, infinitely rigid shafts. Reality is messier.
Things that affect your actual results:
- Gear efficiency: Spur gears typically hit 94-98% per mesh. Worm gears can be anywhere from 50-90%—they trade efficiency for compactness and high ratios.
- Lubrication: Dry gears waste energy as heat and wear out fast. A little grease goes a long way.
- Alignment: Crooked shafts mean the teeth don't mesh cleanly. More friction, more wear, more noise.
- Flex under load: Heavy loads can deflect shafts and gear teeth slightly, which affects the effective ratio at the margins.
For anything mission-critical, test your actual setup rather than trusting the math alone. The calculator gets you in the ballpark—testing confirms you're where you need to be.