Gear Ratio Calculator
Use this gear ratio calculator to determine how the relationship between driver and driven gears affects torque, speed, and output RPM in vehicles, robotics, and industrial machinery.
You can choose between a tooth-based method or a pitch-diameter method, both consistent with engineering standards used in university mechanical design courses and NASA gear-kinematics references.
Ideal for drivetrain design, gear selection, component matching, and educational applications requiring clear, validated calculations.
Tooth-based gear ratio following standard mechanical engineering definitions.
Core inputs
Results
Gear ratio (tooth method)
3
Estimated output RPM
1,000
Methodology
The calculator defines gear ratio as driven ÷ driver, a torque-oriented approach widely used in mechanical design, vehicle powertrain analysis, and robotics.
Tooth-based ratio: driven_teeth ÷ driver_teeth. This method reflects the exact meshing relationship and is preferred for finalized gear sets.
Pitch-diameter-based ratio: driven_pitch_diameter ÷ driver_pitch_diameter. This method is ideal during concept development when tooth counts are not yet chosen.
Output RPM is estimated by dividing input RPM by the gear ratio, assuming ideal rigid gears with negligible friction and perfect meshing.
These kinematic relationships are the same used in engineering education materials from MIT, NASA, SAE, and major mechanical-design university programs.
Worked examples
A 12-tooth driver and 36-tooth driven gear produce a ratio of 3:1, reducing speed from 3000 RPM to about 1000 RPM and tripling torque at the output.
If pitch diameters are 50 mm (driver) and 150 mm (driven), the ratio is again 3:1, demonstrating equivalence when module or diametral pitch is the same.
Key takeaways
This calculator implements both major methods for determining gear ratio and output speed, making it suitable for professional engineering analysis, classroom teaching, and hobbyist drivetrain design.
It provides reliable idealized results, which users should complement with real-world considerations such as backlash, lubrication, efficiency losses, and measurement accuracy.
Further resources
Expert Q&A
Why does this calculator use driven ÷ driver?
This convention emphasizes torque multiplication: ratios greater than 1 increase torque while reducing speed, matching standard engineering analysis.
Are tooth-based calculations more accurate?
Yes. Tooth count fully defines meshing. Pitch diameter is accurate only when gears share identical module or diametral pitch.
Can I use this tool for planetary gear sets?
Planetary systems require additional relationships involving sun, planet, and ring gears. This tool focuses on simple gear pairs.
How accurate are RPM estimates?
They represent ideal kinematics. Real transmissions experience friction, compliance, lubrication losses, and manufacturing tolerances.
Which method should I use for early CAD work?
Use the pitch-diameter method when tooth count is not yet determined.
Sources & citations
- MIT – Gear theory background notes — https://dspace.mit.edu/bitstream/handle/1721.1/36391/2-007Spring-2003/NR/rdonlyres/Mechanical-Engineering/2-007Design-and-Manufacturing-ISpring2003/C614411A-4AAA-4520-8D90-075B85403CF2/0/geartheorybg.pdf
- NASA – Theory of gearing — https://ntrs.nasa.gov/api/citations/19900010277/downloads/19900010277.pdf
- SAE International – Gear ratio fundamentals — https://legacy.sae.org/binaries//content/assets/cm/content/learn/education/motortoycar-samplelessonplan.pdf
- University of Arkansas – Mechanical design: gearing systems — https://uark.pressbooks.pub/mechanicaldesign/chapter/gearing-systems/
- U.S. Department of Energy – Heavy duty engines and drivetrains — https://www.energy.gov/sites/default/files/2022-10/Chapter_10-HD_Engines-Vehicles.pdf