Gear Ratio Calculator
Solve for gear ratio, output speed, or driven teeth using gear teeth or shaft speeds, and see how the ratio affects torque and speed.
Calculation Steps
Practical Drive-Train Guide
Gear Ratio Calculator: From Tooth Counts to Speed and Torque
Use this gear ratio calculator to turn tooth counts, sprocket sizes, and RPM into clear answers for speed, torque, and reduction. This guide explains the equations, when to use each method, and how to sanity-check results before you commit to a design or parts order.
Quick Start: Using the Gear Ratio Calculator Correctly
This gear ratio calculator is built to answer three questions that come up over and over:
- What is the gear ratio from a pair or train of gears or sprockets?
- What is the output speed (RPM or vehicle speed) from a given input RPM and ratio?
- What is the output torque after the gear reduction or overdrive?
The core single-stage equation is:
\[ GR = \frac{N_{\text{driven}}}{N_{\text{driver}}} \]
- 1 Select what you want to solve for: gear ratio, output RPM, vehicle speed, or output torque.
- 2 Enter the basic tooth counts or diameters. For a simple pair: \[ GR = \frac{\text{driven teeth}}{\text{driver teeth}} \] For chains or belts, you can use tooth counts or pulley diameters in the same way.
- 3 If you have a gearbox plus a final drive (for vehicles or machines), enter the gearbox ratio and final drive ratio. The calculator multiplies them: \[ GR_{\text{total}} = GR_{\text{gearbox}} \times GR_{\text{final}} \]
- 4 Enter the input RPM (engine, motor, or crank) and, if you care about vehicle speed, the wheel or tire diameter.
- 5 Review the output RPM, speed, and torque that the calculator reports. Use the quick stats to see things like reduction ratio and mechanical advantage.
- 6 Adjust inputs to explore what-if scenarios: lower gears for acceleration, higher gears for top speed, or a compromise.
- 7 Use the Steps section below the calculator if you want to see the exact equations and substitutions that produced the result.
Tip: In most gear charts, a ratio greater than 1 (for example 4.10:1) means a reduction: output RPM is slower but torque is higher. Ratios less than 1 (for example 0.80:1) mean an overdrive: output spins faster than input.
Warning: Always keep an eye on the units: if diameter is in inches, speed in mph, and RPM is per minute, use the same combination for all related inputs. Mixing metric and imperial is the fastest way to get nonsense results.
Choosing Your Method: Ratio, RPM, or Vehicle Speed
The same gear train can be described in multiple ways. This gear ratio calculator exposes the most common modes so you do not need to remember which equation to rearrange.
Method A — Tooth-Count Gear Ratio
Use this when you know the tooth counts (or pulley diameters) for each meshing pair.
- Simple and fast for sprocket or gear selection.
- Works directly with catalog tooth counts and pitch diameters.
- Extends cleanly to multi-stage reductions.
- Does not directly show vehicle speed or linear motion.
- Requires a separate step to convert RPM to speed or torque.
Single stage: \( GR = N_{\text{driven}} / N_{\text{driver}} \) Multi-stage: \( GR_{\text{total}} = \prod GR_i \)
Method B — RPM-Based Ratio
Use this when you can measure input and output RPM but do not know the teeth.
- Great for reverse-engineering existing machines.
- Simple to validate a design with a tachometer.
- Requires stable speeds (no slip or transient behavior).
- Still needs torque data for mechanical loading checks.
\( GR = \dfrac{\omega_{\text{in}}}{\omega_{\text{out}}} \) with \( \omega_{\text{out}} = \omega_{\text{in}} / GR \)
Method C — Vehicle Speed Mode
Use this to connect engine RPM, gear ratio, final drive, and tire size to a predicted vehicle speed.
- Directly answers “How fast at this RPM?”
- Useful for gear spacing and top-speed checks.
- Requires a realistic tire diameter under load.
- Assumes negligible slip and steady-state rolling.
\[ v = \frac{\pi D_{\text{wheel}} \, n_{\text{engine}}}{GR_{\text{gear}} \, GR_{\text{final}}} \times k \] where \(k\) converts circumference units and minutes to km/h or mph.
What Moves the Number: Key Variables and Trade-Offs
When you play with the gear ratio calculator, these are the variables that drive the output. Use them as “levers” to tune acceleration, top speed, and mechanical loads.
Increasing the driven tooth count (or diameter) or reducing the driver increases the reduction ratio \( GR \). That slows the output speed but multiplies torque.
Multi-stage gearboxes multiply individual stage ratios: \[ GR_{\text{total}} = GR_1 \times GR_2 \times \dots \times GR_n \] Small changes in each stage can produce a large overall effect.
Doubling the input RPM doubles the output RPM and vehicle speed for a fixed ratio. The calculator keeps this relationship explicit.
Larger wheels increase linear distance per revolution: \[ v \propto D_{\text{wheel}} \] This can recover speed lost to a high reduction, at the cost of more torque demand.
Real gear trains lose some torque to friction. If efficiency is \( \eta \), then: \[ T_{\text{out}} = T_{\text{in}} \times GR_{\text{total}} \times \eta \] The calculator’s torque mode can include a typical efficiency to get closer to reality.
Ratios greater than 1.0 are reductions; less than 1.0 are overdrives. Reductions help launch and hill-climb, overdrives help highway cruising.
Worked Examples: From Numbers to Real Behavior
Example 1 — Simple Reduction Gear Pair
- Driver gear teeth: \( N_{\text{driver}} = 12 \)
- Driven gear teeth: \( N_{\text{driven}} = 36 \)
- Input speed: \( n_{\text{in}} = 1800\ \text{RPM} \)
- Input torque: \( T_{\text{in}} = 10\ \text{N·m} \)
- Assumed efficiency: \( \eta = 0.96 \)
Example 2 — Engine RPM to Vehicle Speed
- Engine speed: \( n_{\text{engine}} = 2500\ \text{RPM} \)
- Gearbox ratio (current gear): \( GR_{\text{gear}} = 3.00 \)
- Final drive ratio: \( GR_{\text{final}} = 4.10 \)
- Tire diameter: \( D_{\text{wheel}} = 0.66\ \text{m} \) (≈ 26 in)
- Target output: vehicle speed in km/h and mph
Common Layouts & Variations in Gear Trains
The gear ratio calculator handles any configuration where you can express the overall ratio. This table summarizes typical patterns and what they are used for.
| Configuration | Typical Ratio Range | Applications | Pros | Cons |
|---|---|---|---|---|
| Single pair of gears or sprockets | 0.5:1 to 6:1 | Bicycles, conveyors, simple speed reduction stages | Easy to design, low cost, simple maintenance | Limited ratio range; may require large gears for high reduction |
| Multi-stage gearbox | 10:1 to 200:1 | Industrial gearboxes, robotics joints, winches | High total reduction in compact space | More parts, added friction and backlash, higher cost |
| Overdrive gear set | 0.6:1 to 0.9:1 | Highway cruising gears, fuel economy optimization | Lower engine RPM at speed; quieter and more efficient | Reduced wheel torque; poor for steep climbs and heavy loads |
| Chain or belt drive | 0.5:1 to 8:1 | Motorcycles, go-karts, small machinery | Flexible, easy to swap sprockets or pulleys | Slip (for belts), stretch or wear (for chains); environmental sensitivity |
| Planetary (epicyclic) gear sets | 0.4:1 to 10:1 per set | Automatic transmissions, compact reducers | High power density, multiple ratios in one package | More complex to design; ratio depends on which members are held or driven |
- Decide early if you need fixed or shiftable ratios.
- Use the calculator to compute the total ratio across all stages.
- Check that your ratios allow start-up torque and top speed.
- Confirm that each stage stays inside its rated torque and speed limits.
- Watch cumulative backlash in precision motion systems.
- Document each stage ratio clearly so future changes are easy.
Specs, Logistics & Sanity Checks Before You Lock In a Gear Ratio
The numbers from the gear ratio calculator are only part of the design. You also need to consider ratings, logistics, and how the system will be used in the real world.
Specification Checklist
- Rated torque and power for each gear, sprocket, or pulley.
- Maximum allowable shaft speed and bearing loads.
- Service factor for duty cycle, shock, and environment.
- Backlash tolerance for positioning and noise requirements.
Installation & Logistics
- Space envelope for the largest gear or pulley.
- Center distance constraints and tensioning options.
- Lubrication, sealing, and contamination control.
- Access for inspection and replacement.
Sanity Checks Using the Calculator
- Compare predicted speeds and torques to similar existing machines.
- Run both “ratio from teeth” and “ratio from RPM” modes to cross-check.
- Test extreme operating points (max RPM, worst-case load).
- Verify that motor and controller can supply the demanded torque.
As a rule of thumb, if the calculator suggests a gear ratio that gives either extremely high wheel torque or extremely low engine RPM at cruise, recheck your assumptions and unit selections before releasing drawings.