Gear Ratio Calculator
Calculate the gear ratio between two meshing gears from their tooth counts. Use it when designing drivetrains, selecting motor reduction gears, or analyzing the speed-versus-torque trade-off in any geared system.
Last updated: May 2026
Compare with similar
About this calculator
The formula is: gearRatio = drivenTeeth / drivingTeeth, where drivingTeeth is the number of teeth on the input gear (connected to the power source) and drivenTeeth is on the output gear. A ratio of 2:1 means the driven gear has twice the teeth of the driving gear — it rotates at half the speed but with twice the torque (ideally; minus friction losses). A ratio of 0.5:1 (or 1:2) means the driven gear has half the teeth — it spins twice as fast but with half the torque. Edge cases: zero drivingTeeth causes division by zero (no driving gear). The relationship between input and output: outputSpeed = inputSpeed / gearRatio; outputTorque = inputTorque × gearRatio × efficiency, where efficiency is typically 92–98% for spur and helical gears, 80–95% for worm gears (more loss). Compound gear trains multiply ratios: two stages of 5:1 each give 25:1 total reduction. Common applications: car transmissions 3:1 to 4:1 first gear reduction (boosts engine torque to wheels at startup); 1:1 fourth gear (direct drive); 0.7:1 fifth gear (overdrive, reduces engine RPM for highway fuel economy). Electric motor reducers commonly 10:1 to 100:1 (servo motors and stepper motors are high-speed/low-torque; reducers convert to robot joint requirements). Bicycle drivetrains: front chainring/rear cog defines gear ratio; "gear inches" = wheel diameter × (front teeth/rear teeth). Higher numbers mean higher speed per crank revolution but harder pedaling. The gear ratio determines the trade-off: high ratio = high torque, low speed (excavator boom hydraulics, bottle openers, garage door openers); low ratio (or 1:1) = high speed, low torque (drill bits, CNC spindle drives, fan blades). Pitch (tooth size — module in metric, diametral pitch in imperial) must match between meshing gears; ratio is independent of pitch but mounting geometry depends on gear sizes that result from pitch × tooth count.
How to use
Example 1 — Manual transmission first gear. Engine input gear 18 teeth; first gear cluster 54 teeth. Enter drivingTeeth 18, drivenTeeth 54. Result: 54/18 = 3.0:1 reduction. ✓ Engine RPM is divided by 3 at the transmission output; engine torque is multiplied by 3 (minus efficiency). For an engine making 200 lb-ft torque at 3,000 RPM, transmission output is 600 lb-ft at 1,000 RPM. Combine with the differential ratio (typically 3.5:1 to 4.5:1 final drive) for total 10:1 to 13:1 from engine to wheels in first gear — high enough torque to climb steep grades from a stop without stalling. Example 2 — Robot servo with reducer. Motor 3,000 RPM, joint requires 30 RPM and 50 N·m torque. Required ratio = 3000/30 = 100:1 reduction. If using a planetary reducer with three 4.64:1 stages: 4.64³ = 99.9 ≈ 100. Motor torque needed = 50/100/0.92 (efficiency) = 0.54 N·m at the motor. ✓ Verify motor specifications can deliver 0.54 N·m continuously at 3,000 RPM; this is a small motor (50–100W typical). Selecting actual standard reducers: harmonic drives (Harmonic Drive, CSF) at 50:1 to 320:1; planetary (Apex, Wittenstein) at 5:1 to 100:1 per stage; cycloidal (Sumitomo, Nabtesco) at 30:1 to 200:1. Each type has different backlash, efficiency, and cost characteristics.
Frequently asked questions
What does gear ratio physically do to speed and torque?
It trades off speed against torque while keeping power (ideally) constant. Power = torque × angular velocity; in an ideal frictionless gear, input power equals output power. So if you reduce speed by a factor of N (gear ratio N:1), you increase torque by approximately the same factor N. Real gears have friction losses (2–10% per mesh for spur/helical gears, 5–20% for worm gears), so actual output torque is gearRatio × inputTorque × efficiency. Example: a 10:1 reducer with 95% efficiency converts 1 N·m, 1000 RPM input to 9.5 N·m at 100 RPM output. The trade-off is fundamental — you cannot make a passive gear set increase both speed and torque simultaneously. To increase both, you need active power input (motor, engine). The trade-off explains many design choices: car transmissions use low gears (high reduction) for starting from a stop (high torque needed at low speed), and high gears (low reduction or overdrive) for cruising (lower torque needed at high speed). Electric vehicles, with their wide-torque motors, often use single-speed reducers — the motor itself adjusts to load without needing gear changes.
What types of gears are commonly used?
Several types each with specific strengths. Spur gears: straight teeth parallel to the shaft axis; simplest, cheapest, efficient (~98%), but noisy at high speed; widely used in low-to-medium speed industrial machinery. Helical gears: teeth angled to the axis; quieter and stronger than spur at high speed; produce axial thrust load that must be supported by bearings; common in automotive transmissions, gearboxes. Bevel gears: teeth on conical surfaces; transmit power at 90° (or other angles) between shafts; used in differentials, right-angle drives. Worm gears: a "worm" (screw-like gear) drives a "wormwheel"; high reduction ratios (10:1 to 100:1) in a single mesh; self-locking design possible (can't be back-driven); lower efficiency (50–95%) due to sliding contact. Planetary gears: sun gear in the center, planet gears orbiting, ring gear outside; compact high-reduction (3:1 to 10:1 per stage); used in automatic transmissions, electric motor reducers. Harmonic drive: thin-walled flexspline deformed by wave generator inside circular spline; zero backlash, high reduction (50:1 to 320:1); used in robotics. Cycloidal: eccentric input drives a lobed disc against pins; high shock tolerance, low backlash; industrial. Selection criteria: speed, torque, efficiency, backlash, noise, cost, size, mounting orientation.
How do I select the right gear ratio for my application?
Work backward from output requirements. Step 1: Define required output speed and torque at the load. Step 2: Calculate output power = torque × angular velocity (in consistent units). Step 3: Select a motor that exceeds output power by a margin for losses (typically 1.5–2× margin for industrial; less for consumer products). Step 4: Calculate ratio = motor speed / required output speed. Step 5: Verify that the resulting torque (motor torque × ratio × efficiency) meets or exceeds required output torque with safety margin. Step 6: Select a standard reducer with the calculated ratio; not all ratios are commercially available. Common available ratios: 3:1, 5:1, 10:1, 15:1, 20:1, 30:1, 50:1, 100:1 for typical industrial reducers. For higher ratios, stack reducers (e.g., 10:1 × 10:1 = 100:1). Step 7: Verify mechanical fit (input shaft size and orientation matches motor; output shaft size and orientation matches load; mounting space adequate). Step 8: Check thermal limits — high reduction at high power produces heat in the reducer; some reducers need cooling at continuous high load. Step 9: Check life and reliability — gear life depends on tooth contact stress; published ratings are for specific load and speed combinations. For variable-load applications, consult manufacturer's life calculator software.
What are the most common gear ratio mistakes?
The biggest is forgetting to multiply ratios in compound trains; two stages of 5:1 each is 25:1, not 10:1. The second is confusing input and output orientations; the ratio you calculate may be the "speed reducer" ratio (output speed = input/ratio) or the "torque multiplier" ratio (output torque = input × ratio). For a 4:1 reduction, "4:1 reducer" means input rotates 4 times for each output rotation. The third is mismatching tooth pitches; gears with different module/diametral pitch don't mesh properly. Use only matching-pitch gears or convert to differential. The fourth is over-estimating efficiency in worm gear systems; worm gears can be 50–90% efficient depending on lead angle and lubrication — much less efficient than spur or helical gears. The fifth is failing to account for backlash; even high-quality gears have some clearance between mating teeth, allowing rotation reversal without immediate motion transfer — critical for positioning applications. The sixth is mismatching the application duty cycle to gear ratings; gears rated for "intermittent" 1000-hour service won't last 5000 hours of continuous use. The seventh is selecting gears that operate near maximum allowable speed; pitch line velocity over 30 m/s requires special lubrication and analysis. The eighth is forgetting thermal limitations; high-power continuous service heats reducers, and many manufacturers de-rate at elevated temperatures. The ninth is using cheap reducers in safety-critical applications where backlash, reliability, and overload capacity matter; planetary reducers and harmonic drives cost more but provide better predictable performance. The tenth is ignoring shaft alignment in coupled gear/motor pairs; misalignment dramatically reduces life.
When should I not use this calculator?
Skip it for friction-drive systems (rollers, friction wheels, friction discs) where there are no teeth and the "ratio" depends on diameter rather than tooth count; use diameter ratio instead. It is the wrong tool for belt and chain drives; while they also produce speed/torque ratios, the math involves pulley diameters and timing belt teeth differently than gear teeth. Use belt-drive-specific calculators. Do not use it for continuously variable transmissions (CVTs) where the ratio varies continuously based on system state; CVT analysis requires more complex modeling. For traction drives and hydraulic transmissions, the speed/torque relationship is determined by fluid mechanics rather than mechanical gear teeth. For very high-ratio transmissions (>1000:1) where you need extreme reduction, dedicated harmonic drives or cycloidal reducers should be selected from manufacturer specifications rather than calculated from tooth counts. For automotive transmissions, the published "gear ratios" include both internal gear ratio and external coupling, often with synchronizer and clutch dynamics; use automotive-specific analysis. For backlash-critical applications (CNC machining, robotics with sub-arcminute positioning), tooth-count ratio is just one input; specific gear design and quality factors dominate. And for thermal and lubrication analysis at high power, additional manufacturer-specific data is needed beyond the tooth count math.