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Calculate gear ratio, output shaft RPM, output torque, mechanical advantage, and power loss for any gear pair. Find transmission ratio from driver and driven gear teeth counts for motors, gearboxes, and drive systems.
Gear ratios trade speed for torque while conserving power (minus friction losses). A 4:1 ratio means the output shaft turns at 1/4 input speed but produces 4 times the input torque. This fundamental relationship allows electric motors and engines to match their speed-torque characteristics to the load requirement.
| Application | Ratio | Notes |
|---|---|---|
| Car 1st gear | 3.5-4.0:1 | High torque for starting |
| Car top gear | 0.7-1.0:1 | High speed, fuel economy |
| Bicycle low | 0.5-1.0:1 | Hill climbing |
| Industrial reducer | 5:1 to 100:1 | Torque multiplication |
| Worm gear | 10:1 to 300:1 | Self-locking, compact |
| Spur gear efficiency | 95-99% | Per mesh pair |
This free engineering calculator uses established formulas from mechanical, civil, electrical, and chemical engineering. Results are computed instantly in your browser with no data sent to any server. For professional engineering applications, always verify calculations independently and have results reviewed by a qualified engineer. Use the Copy button to save results and Share to send this calculator to colleagues.
Gears transmit rotational power between shafts while changing speed and torque. The gear ratio is simply the ratio of teeth on the driven gear to teeth on the driver gear. A 20-tooth driver meshing with an 80-tooth driven gear produces a 4:1 ratio — output turns at 1/4 speed with 4 times the torque (minus efficiency losses). This principle is used in virtually every machine from wristwatches to wind turbines.
| Type | Shafts | Efficiency | Application |
|---|---|---|---|
| Spur gears | Parallel shafts | 95-99% | Simple, common, noisy at speed |
| Helical gears | Parallel/crossed | 95-99% | Quieter, handles more load |
| Bevel gears | Intersecting | 93-97% | Right-angle drives |
| Worm gears | Perpendicular | 50-90% | High ratios, self-locking |
| Planetary gears | Coaxial | 95-98% | Compact, high ratios, automatic transmissions |
| Rack and pinion | Rotary to linear | 95-98% | Steering, linear positioning |
Steps for selecting motor and gearbox: (1) Determine required output: speed (RPM) and torque (N·m). (2) Select motor: rated speed and torque from motor datasheet. (3) Calculate required gear ratio: GR = Motor RPM / Required output RPM. (4) Verify output torque = Motor torque x GR x efficiency meets load. (5) Check efficiency across the full operating range. (6) Consider starting torque requirements — some loads need 200-300% of running torque to start.
Multiple gear pairs in series (compound gear train) multiply individual ratios to achieve very large total ratios. Total GR = GR1 x GR2 x GR3. Total efficiency = η1 x η2 x η3. A 3-stage spur gearbox with 4:1 per stage: total GR = 64:1, total efficiency = 0.97^3 = 91.3%. Planetary gearboxes achieve high ratios (up to 100:1) in a compact package because the internal gear, planet gears, and sun gear all share the load.
Engineering calculations are the foundation of every designed system — from the bolts holding a bridge together to the pipe carrying water to your tap. These free calculators cover the most commonly needed engineering formulas across civil, mechanical, electrical, and chemical engineering disciplines. All calculations use standard SI units and established engineering formulas from recognized references.
Engineering design always includes safety factors to account for material variability, load uncertainty, construction tolerances, and progressive deterioration. Typical safety factors: structural steel bending 1.67 (ASD), concrete compression 1.5-2.0, bolts in tension 2.0-3.0, pressure vessels 3.5-4.0. Always verify that your design complies with applicable local codes, national standards, and industry regulations before construction or installation.
Supplement these calculators with free engineering references: AISC Steel Construction Manual (steel design), ACI 318 (concrete design), NFPA 70 NEC (electrical), ASHRAE Fundamentals Handbook (HVAC), and Machinery Handbook (mechanical). Engineering toolboxes, NIST databases, and professional society websites provide free access to many standards and reference materials for non-commercial educational use.