Gear Ratio Calculator – Complete Guide To Gears, Sprockets, RPM And Speed
Gear ratios are at the heart of every drivetrain. From bicycles and motorcycles to cars, karts, industrial machines and robotics, gears and sprockets trade speed for torque or torque for speed. This Gear Ratio Calculator gives you a fast way to turn tooth counts and RPM values into meaningful numbers for planning and troubleshooting.
The tool can handle simple single-stage gear pairs, chain and sprocket drives, multi-stage reductions, RPM conversions and approximate wheel speeds. It is designed to be readable for beginners while still being useful for hobbyists, mechanics and engineers who want quick back-of-the-envelope answers.
1. Basic Gear Ratio Definition
For a simple pair of gears with a small driver gear and a larger driven gear, the basic gear ratio is defined as the number of teeth on the driven gear divided by the number of teeth on the driver gear:
If the driver gear has 15 teeth and the driven gear has 45 teeth, the ratio is 45 ÷ 15 = 3.0. This is often called a 3:1 reduction. The driven gear turns at one third of the speed of the driver, but torque at the driven gear is multiplied by roughly three times (ignoring losses).
When the driven gear is smaller than the driver, the ratio is less than 1.0. In this case, the driven shaft spins faster than the driver and torque is reduced. This is sometimes described as an overdrive ratio.
2. Speed And Torque In A Gear Pair
In an ideal gear pair with no losses, power is conserved. Power is torque multiplied by rotational speed, so when one goes down, the other goes up:
- Speed ratio ≈ 1 ÷ gear ratio
- Torque ratio ≈ gear ratio
Using the example above with a 3:1 reduction:
- The driven gear rotates at one third of the driver speed.
- The driven shaft sees approximately three times the torque of the driver shaft.
Real systems have friction and other losses, so actual torque at the driven shaft is slightly lower than the ideal calculation. However, the ratio still provides an excellent first estimate and is the main design handle for matching speed and torque to the job.
3. Using The Basic Gear Ratio Tab
The Basic Gear Ratio tab in the calculator focuses on a single driver–driven pair.
- Enter the number of teeth on the driver gear in the Driver Gear Teeth field.
- Enter the number of teeth on the driven gear in the Driven Gear Teeth field.
- Select your preferred direction interpretation: reduction or overdrive.
- Select Compute Gear Ratio to calculate the results.
The calculator then reports:
- Gear Ratio: driven teeth ÷ driver teeth.
- Speed Factor: how much faster or slower the driven shaft turns relative to the driver.
- Torque Factor: approximate torque multiplication or reduction factor.
- Text Summary: a short sentence describing the result in everyday language.
This is ideal when you are sketching a simple gearbox, checking a bicycle gear combination or estimating what a single pair of sprockets will do in a small machine.
4. Chain Drives And Multi-Stage Gear Trains
Many real-world systems use more than one gear or sprocket pair in sequence. For example, a motorcycle might have a primary reduction, a gearbox ratio and a final chain drive. Each stage has its own ratio, and the overall ratio is the product of all of them:
If the first stage is 3:1 and the second stage is 2:1, the combined ratio is 3 × 2 = 6:1. The output turns at one sixth of the input speed, with roughly six times the torque, again ignoring losses.
The Chain & Multi-Stage tab lets you enter up to three stages by providing driver and driven teeth for each stage. Empty or zero rows are skipped. The calculator shows the individual stage ratios and the combined overall ratio, along with speed and torque factors.
5. Converting Between Input And Output RPM
Once you know the gear ratio, converting RPM is straightforward. With a ratio defined as driven ÷ driver:
- Output RPM = Input RPM ÷ gear ratio (for a reduction).
- Input RPM = Output RPM × gear ratio.
The Speed & RPM tab handles both directions. You choose which RPM is known (input or output), enter the value and the gear ratio, and the calculator returns the missing RPM along with a note about whether the system is acting as a reduction or overdrive.
This is useful when you know a motor’s rated RPM and want to see what shaft speed you will get, or when you start with a desired output speed and work backwards to select an appropriate ratio.
6. From Engine RPM To Vehicle Speed
For vehicles, it is common to think in terms of road speed instead of just wheel RPM. To estimate speed from engine RPM, you need three ingredients:
- Engine RPM.
- Overall drive ratio between engine and wheels.
- Wheel or tire diameter to find circumference.
The wheel rotates once per overall ratio turns of the engine, so:
The distance traveled per wheel revolution is the wheel circumference, which is π × diameter. Combining these pieces gives an approximate linear speed in km/h or mph. The Wheel Speed tab in the calculator performs this conversion using wheel diameter in inches, returning wheel RPM, speed in km/h and speed in mph.
This is a convenient way to see how changing tire size or final drive ratio will affect cruising RPM or top speed for a given gear.
7. Comparing Different Gear Ratios
When tuning a machine or vehicle, you often want to compare alternative gear sets. Lower (numerically higher) ratios provide more torque at the wheels but lower top speed for a given engine RPM. Higher (numerically lower) ratios do the opposite.
The Ratio Comparison tab lets you enter up to five driver–driven pairs. For each set, the calculator finds the gear ratio, classifies it as:
- Reduction (ratio > 1.0).
- Overdrive (ratio < 1.0).
- Direct 1:1 (ratio ≈ 1.0).
It then highlights which set provides the highest torque multiplication and which provides the highest output speed (lowest ratio), and summarises how many sets fall into each category. This helps you decide which combination best fits low-speed pulling power versus high-speed cruising.
8. Practical Tips And Limitations
Gear ratio calculations are powerful, but a few practical issues should be kept in mind:
- Real systems have efficiency losses from friction, flex and windage, so actual torque is slightly lower than ideal.
- Gears and chains have minimum tooth counts to avoid undercutting and poor engagement, especially for very small sprockets.
- Vehicle speed estimates assume no tire slip and use a nominal unloaded tire diameter; real-world speed will differ slightly.
- Backlash, compliance and other dynamic effects can influence behaviour even with the same static ratio.
The Gear Ratio Calculator is therefore best viewed as a design and learning tool for quickly understanding how changes in teeth counts, ratios and wheel sizes shift the balance between speed and torque.
Gear Ratio Calculator FAQs
Frequently Asked Questions
Key questions about gear ratio definitions, reduction vs overdrive, multi-stage drives and how to interpret RPM and wheel speed results from this Gear Ratio Calculator.
For a simple gear pair, gear ratio is defined as driven teeth divided by driver teeth. If the driver has 12 teeth and the driven gear has 36 teeth, the ratio is 36 ÷ 12 = 3.0. This is a 3:1 reduction, meaning the driven gear turns at one third of the driver speed and sees roughly three times the torque.
A reduction ratio is greater than 1.0 and slows the output while increasing torque. An overdrive ratio is less than 1.0 and speeds up the output while reducing torque. A 1.0 ratio is direct drive, where input and output rotate at the same speed. The calculator classifies ratios and explains whether you are gaining speed or torque in each case.
For multi-stage systems, the calculator multiplies stage ratios together. If stage one has a 2:1 reduction and stage two has a 3:1 reduction, the overall ratio is 2 × 3 = 6:1. You can enter up to three stages in the Chain & Multi-Stage tab, and the tool will show both the individual stage ratios and the combined overall ratio along with speed and torque factors.
The RPM and wheel speed calculations are based on ideal geometric relationships and assume no slip, perfect engagement and a fixed wheel diameter. Real-world results will vary slightly because of tire deformation, slip, dynamic loading and drivetrain losses, but the estimates are usually accurate enough for planning and comparison purposes.
Yes. As long as you know the relevant teeth counts and, for wheel speed, an effective wheel diameter, the same formulas apply to bicycles, e-bikes, scooters, karts, small robots and many other systems. Simply treat each chainring–sprocket or pulley pair as a gear stage and use the appropriate tab of the calculator to combine them.
A physical gear or sprocket must have a positive number of teeth. A gear ratio of zero or a negative value has no meaning in this context, and would create division-by-zero or sign problems in the formulas. To avoid misleading results, the calculator checks for non-positive values and shows an error message instead of trying to compute with invalid inputs.