Gear Ratio Calculator
Calculate mechanical gear ratios from tooth counts for any gear pair or compound gear train. Instantly determine output RPM, torque multiplication, and speed reduction — essential for engineering design, robotics, automotive tuning, and industrial machinery.
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What is Gear Ratio?
A gear ratio describes the rotational speed relationship between two meshing gears, determined by dividing the number of teeth on the driven (output) gear by the teeth on the driving (input) gear. A 60-tooth driven gear meshed with a 20-tooth driving gear produces a 3:1 ratio, meaning the input shaft must rotate three times for every single output rotation. This trades speed for torque — the output turns three times slower but delivers three times the turning force.
Gear ratios are the foundation of mechanical power transmission in virtually every machine: automotive transmissions, industrial gearboxes, wind turbines, conveyor systems, clock mechanisms, bicycle drivetrains, and robotic actuators. By selecting appropriate gear ratios, engineers precisely match a motor or engine's speed and torque output to the application's requirements without changing the power source.
Формулы и Используемые Уравнения
В калькуляторе заложены 5 основных уравнений:
1 Gear Ratio ▼
Driven (60 teeth) / Driver (20 teeth) = 3:1 ratio.
2 Output RPM ▼
Input 3600 RPM with 3:1 ratio: Output = 3600 / 3 = 1200 RPM.
3 Compound Gear Train Ratio ▼
Two stages of 3:1 and 4:1: Overall = 3 × 4 = 12:1 total reduction.
Explore all calculation options on the Калькулятор Отношений home page.
Как Пользоваться Калькулятором
Чтобы использовать этот Калькулятор Отношений, выполните 3 простых шага:
Введите Данные
Введите известные числа в поля ввода. Оставьте одно поле пустым — калькулятор вычислит это неизвестное значение.
Выберите Режим
Выберите режим работы — Решение пропорций, Упрощение отношений или Масштабирование. В каждом режиме используются свои математические формулы.
Получите Результат
Нажмите кнопку Вычислить. На экране отобразится ответ с цветной шкалой отношения, круговой диаграммой и пошаговым решением.
Примеры Задач с Пошаговыми Решениями
Вот 3 практических примера расчетов с подробным математическим описанием действий:
Ввод 1 40-tooth gear driven by 10-tooth pinion
Ввод 2 Motor at 1800 RPM through 5:1 gearbox
Ввод 3 Two-stage reducer: 3:1 and 4:1
Часто Задаваемые Вопросы
What does a higher gear ratio mean? ▼
A higher gear ratio (like 5:1 vs. 2:1) means more speed reduction and more torque multiplication. The driving gear must spin more times per output revolution. Higher ratios are used for starting from a stop (first gear in a car) or for high-torque, low-speed applications like winches and lifts.
How do compound gear trains work? ▼
Compound trains stack multiple gear pairs on shared shafts. Each pair's ratio multiplies with the others. Two stages of 3:1 and 4:1 give 12:1 overall. Three stages of 3:1 each give 27:1. This allows massive speed reductions in a compact package without requiring extremely large gears.
What is a gear reduction vs. overdrive? ▼
A gear reduction means the output is slower than the input (ratio > 1:1), delivering more torque. An overdrive means the output is faster than the input (ratio < 1:1), delivering less torque. Car transmissions use reductions in low gears for acceleration and overdrive in top gear for highway cruising.
How do I calculate gear ratio for a specific output speed? ▼
Divide the motor RPM by your desired output RPM. To get 500 RPM from a 3,000 RPM motor: Ratio = 3,000 ÷ 500 = 6:1. Then select gear teeth: a 12-tooth driver and 72-tooth driven gear gives exactly 6:1.
Does gear ratio affect power output? ▼
No. Power (watts = torque × angular speed) is conserved through an ideal gear train. A 3:1 ratio triples torque but reduces speed by one-third, keeping power constant. Real gear trains lose 1-3% per stage to friction, so output power is slightly less than input power.
What gear ratio do I need for a specific torque? ▼
Divide your required output torque by the motor's available torque. If you need 50 Nm and your motor produces 5 Nm, you need a 10:1 gear ratio (plus margin for friction losses). Select a ratio of 11:1 to 12:1 to ensure adequate torque after efficiency losses.
How does gear module (tooth size) affect the ratio? ▼
Gear module (metric) or diametral pitch (imperial) defines the tooth size but does not change the ratio. A 20-tooth and 60-tooth gear give a 3:1 ratio regardless of tooth size. However, both gears in a pair must use the same module to mesh properly.
What is the efficiency of a typical gear stage? ▼
Spur gears: 94-98% per stage. Helical gears: 95-99%. Worm gears: 40-90% (depends on lead angle). Bevel gears: 93-97%. For multi-stage calculations, multiply the efficiencies: 3 stages at 97% = 0.97³ = 91.3% overall efficiency.
Can I achieve any gear ratio with standard gears? ▼
Not exactly. Standard gears come in specific tooth counts (typically 12 to 150+ teeth). The achievable ratios depend on available tooth count combinations. For precise non-standard ratios, use compound gear trains where multiplied ratios can approximate nearly any value.
How do planetary gear sets differ from simple gear trains? ▼
Planetary (epicyclic) gear sets use a sun gear, ring gear, and planet gears orbiting between them. They achieve high reduction ratios in a compact, coaxial package. Ratios of 3:1 to 12:1 per stage are common. They are used in automatic transmissions, power tools, and robotic joints.
What is the gear ratio of a bicycle? ▼
Bicycle gear ratio = front chainring teeth ÷ rear cassette teeth. A 50-tooth chainring with a 25-tooth rear cog gives a 2:1 ratio, meaning the rear wheel turns twice per pedal revolution. Multiplied by wheel circumference, this determines the distance traveled per pedal stroke (gear inches).