Calculate output RPM from gear ratio and motor speed, find required ratio for a target RPM, or determine needed motor speed. Multi-stage support with standard motor speed reference.
When selecting a gearbox for an electric motor, the most common question is: "What RPM will I get at the output?" The answer is simple — divide the motor speed by the gear ratio — but the practical engineering involves matching standard motor speeds to application requirements, accounting for multi-stage reductions, and verifying the torque and power budgets.
This calculator works in three directions: compute output RPM from a known motor speed and gear ratio, find the required gear ratio to achieve a target output RPM, or determine what motor speed is needed given a fixed gearbox and desired output. Each mode includes torque and power calculations with efficiency losses.
The standard motor speed reference table (NEMA/IEC), application RPM guide, and ratio comparison chart make this tool ideal for quick gearbox selection in industrial, manufacturing, and automation applications. Multi-stage support handles compound gear trains up to 3 stages with independent ratios and cumulative efficiency.
Gearbox selection requires matching motor catalogs to application needs. This calculator bridges the gap: enter your motor speed and desired output, get the required ratio instantly. The motor speed table with pre-calculated outputs eliminates catalog-flipping, and multi-stage support handles complex drive trains. Keep these notes focused on your operational context.
Output RPM: RPM_out = RPM_in / GR Required Ratio: GR = RPM_in / RPM_target Required Input RPM: RPM_in = RPM_target × GR Output Torque: τ_out = τ_in × GR × η^n (n = number of stages) Power: P = τ × 2π × RPM / 60 (watts) Multi-stage: GR_total = GR₁ × GR₂ × GR₃ RPM_out = RPM_in / GR_total
Result: Output: 175 RPM, torque multiplied 10× (190 N·m from 20 N·m input)
A standard 4-pole motor at 1750 RPM with a 10:1 gearbox: Output = 1750/10 = 175 RPM. Input torque of 20 N·m becomes 20 × 10 × 0.95 = 190 N·m at the output (95% gearbox efficiency). Power in: 20 × 2π × 1750/60 = 3,665 W (4.9 hp). Power out: 3,482 W after 5% friction loss.
The typical gearbox selection process: (1) Determine required output RPM and torque from the application. (2) Calculate required power = torque × angular velocity. (3) Select a motor with sufficient power (accounting for gearbox efficiency). (4) Calculate gear ratio = motor RPM / desired RPM. (5) Select a catalog gearbox with the nearest ratio. (6) Verify output torque meets requirements at the selected ratio.
For high ratios, split the total ratio into stages of roughly equal ratio. The most efficient distribution is geometric: if total ratio is R with n stages, each stage should be approximately R^(1/n). For a 100:1 ratio in 3 stages: 100^(1/3) ≈ 4.64:1 each. In practice, stages may be unequal due to available gear sizes, and the first stage often uses the smallest ratio (highest speed, smallest torque) to minimize gear size.
Modern drive systems often combine a fixed-ratio gearbox with a variable frequency drive (VFD) for fine speed control. The gearbox handles the bulk reduction (e.g., 10:1), while the VFD adjusts motor speed ±50% around nominal. This combination provides a wide speed range (e.g., 87.5-262.5 RPM) with high efficiency and precise control — far superior to mechanical variable-speed drives.
AC induction motors run slightly slower than synchronous speed due to slip. A 4-pole motor on 60 Hz has synchronous speed of 1800 RPM but runs at about 1725-1770 RPM under load (2-4% slip). The "1750 RPM" rating is a typical full-load speed.
Higher ratios mean more gearbox stages, more cost, and more efficiency losses. Lower ratios need a larger (more expensive) motor. The optimum balances motor cost, gearbox cost, efficiency, and available space. For ratios above 50:1, multi-stage gearboxes are almost always needed.
Yes — belt and pulley drives follow the same ratio rule: Output RPM = Input RPM × (Driver Pulley Diameter / Driven Pulley Diameter). The efficiency per stage is typically 95-98% for V-belts and 98-99% for timing belts.
Standard catalog gearboxes come in fixed ratios (3:1, 5:1, 10:1, 15:1, 20:1, etc.). For non-standard ratios, use multi-stage arrangements, combine a gearbox with a VFD (variable frequency drive) to adjust motor speed, or use custom gear sets.
A VFD adjusts motor speed by changing the supply frequency. A motor at 30 Hz runs at half the 60 Hz speed. This effectively gives a continuously variable "electronic gear ratio" that can complement a fixed gear ratio gearbox for fine speed control.
A single 50:1 gear pair would need a driven gear 50× the diameter of the driver — impractically large. Two stages of about 7:1 each (7 × 7 = 49) use much smaller gears. The rule of thumb: keep each stage under 6-8:1 for spur gears.