What Is Gear Ratio?
Gear ratio is the relationship between two meshing gears that determines how rotational speed and torque are transferred from one to the other. It is calculated by comparing the number of teeth on the driven gear (output) to the number of teeth on the driving gear (input).
A gear ratio of 3:1 means the driving gear (input) must rotate 3 times for the driven gear (output) to complete one full rotation. The output is 3 times slower, but it delivers 3 times more torque. This trade-off between speed and torque is the fundamental principle behind every gear system, from bicycle transmissions and car gearboxes to the precision gear trains inside electric linear actuators.
Understanding gear ratio is essential for anyone designing, selecting, or troubleshooting mechanical systems. It tells you exactly how much speed you will gain or lose, and how much force (torque) your output shaft will produce.
Gear Ratio Formula
The basic gear ratio formula is:
Or equivalently:
Where:
- Ndriven = number of teeth on the output (driven) gear
- Ndriver = number of teeth on the input (driving) gear
Worked example: A motor drives a 15-tooth gear (driver) which meshes with a 60-tooth gear (driven).
This means the motor shaft must rotate 4 times for the output shaft to rotate once. Output speed is one-quarter of input speed, but output torque is four times the input torque (minus friction losses).
If the ratio is less than 1 (for example, a 40-tooth driver meshing with a 20-tooth driven gear = 0.5:1), the output spins faster than the input but with less torque. This is called overdrive.
Gear Ratio Calculator
Enter the number of teeth on your driver and driven gears to calculate the gear ratio, output speed, and output torque. For multi-stage systems, calculate each stage and multiply the ratios together (see Multi-Stage section below).
Driver gear teeth (input):
Driven gear teeth (output):
Input speed (optional): RPM
Input torque (optional): N·m or lb·in
Gear efficiency: %
Speed, Torque, and Mechanical Advantage
Gears trade speed for torque, or torque for speed. This trade-off is governed by the conservation of power — the power going in (minus friction losses) equals the power coming out. Since Power = Torque × Speed, if speed goes down, torque must go up proportionally.
The key formulas are:
Output Speed = Input Speed ÷ Gear Ratio
Output Torque = Input Torque × Gear Ratio × Efficiency
Mechanical Advantage = Gear Ratio (torque multiplier)
Worked example: A motor spins at 3,000 RPM and produces 0.5 N·m of torque. It drives through a 50:1 gear reduction with 90% overall efficiency.
- Output speed: 3,000 ÷ 50 = 60 RPM
- Output torque: 0.5 × 50 × 0.90 = 22.5 N·m
The gear system slowed the motor by 50× but multiplied its torque by 45× (50× ratio minus 10% friction loss). This is exactly what happens inside a linear actuator — a small, fast motor is geared down to produce the high force and controlled speed needed to push or lift a load.
Multi-Stage Gear Trains
When a single gear pair cannot achieve the required reduction (or the gears would be impractically large), multiple stages are used in series. Each stage multiplies the ratio of the previous stage.
Worked example: A three-stage gearbox with ratios of 4:1, 5:1, and 3:1:
Efficiency also compounds across stages. If each stage is 97% efficient:
This is why multi-stage planetary gearboxes are preferred in actuators — they achieve very high ratios in compact packages while maintaining efficiency above 90%.
Types of Gears
Different gear types serve different purposes. The type of gear affects noise, efficiency, load capacity, and the direction of power transmission.
Spur Gears
The simplest and most common gear type. Teeth are straight and parallel to the shaft axis. Spur gears transmit power between parallel shafts. They are inexpensive, easy to manufacture, and highly efficient (94–98% per mesh). The trade-off is noise — spur gears are louder than helical gears at high speeds because teeth engage suddenly rather than gradually. Most small actuators and gear motors use spur gears.
Helical Gears
Similar to spur gears but with teeth cut at an angle (helix) to the shaft. This causes teeth to engage gradually, resulting in smoother and quieter operation. Helical gears handle higher loads and speeds than spur gears. The downside is axial thrust — the helix angle creates a force along the shaft that requires thrust bearings. Efficiency is 95–98% per mesh. Common in automotive transmissions and industrial gearboxes.
Planetary (Epicyclic) Gears
A planetary system has a central sun gear, multiple planet gears that orbit around it, and an outer ring gear. The planets distribute load across multiple teeth simultaneously, giving planetary systems excellent torque capacity in a compact package. Efficiency is 95–97% per stage. Planetary gear trains are widely used inside actuators, robotics, and automatic transmissions.
Worm Gears
A worm gear consists of a screw-shaped worm that meshes with a toothed worm wheel. Worm gears achieve very high reduction ratios in a single stage (5:1 to 100:1+) and transmit power between perpendicular shafts. They are self-locking — the output cannot back-drive the input, which is useful for holding a load in position without a brake. The drawback is low efficiency (40–90%) due to high sliding friction. Common in conveyor systems, lifting jacks, and some actuator designs.
Bevel Gears
Bevel gears transmit power between shafts at an angle, most commonly 90°. The teeth are cut on the conical surface of the gear. Straight bevel gears are simpler; spiral bevel gears are quieter and handle higher loads. Efficiency is 93–97%. Common in differential drives, rotary actuators, and right-angle gearboxes.
Rack and Pinion
A rack is a flat, toothed bar that meshes with a circular gear (the pinion). Turning the pinion converts rotational motion into linear motion along the rack, or vice versa. Rack and pinion systems are used in steering mechanisms, CNC machines, and some linear motion systems as an alternative to lead screws.
Gear Efficiency Reference Table
| Gear Type | Efficiency (per mesh) | Typical Ratio Range | Shaft Orientation | Self-Locking? |
|---|---|---|---|---|
| Spur | 94–98% | 1:1 to 6:1 | Parallel | No |
| Helical | 95–98% | 1:1 to 10:1 | Parallel | No |
| Planetary | 95–97% per stage | 3:1 to 10:1 per stage | Coaxial (inline) | No |
| Worm | 40–90% | 5:1 to 100:1+ | Perpendicular | Yes (at high ratios) |
| Bevel (straight) | 93–97% | 1:1 to 5:1 | Perpendicular | No |
| Bevel (spiral) | 95–98% | 1:1 to 5:1 | Perpendicular | No |
| Rack & Pinion | 90–97% | N/A (linear conversion) | Rotary → Linear | No |
Gears Inside Linear Actuators
Every electric linear actuator contains a gear train that converts the motor's high-speed, low-torque rotation into the low-speed, high-force linear motion you need. Here is how it works:
The DC motor spins at 3,000–6,000+ RPM. The motor shaft drives a spur or planetary gear train that reduces the speed by a factor of 20:1 to 100:1 or more. The output of the gear train drives a lead screw (a threaded rod). A nut on the lead screw converts the rotation into straight-line push/pull motion of the actuator rod.
The gear ratio directly determines the actuator's force and speed specifications:
- Higher gear ratio (more reduction) = more force, slower speed
- Lower gear ratio (less reduction) = less force, faster speed
This is why FIRGELLI offers actuators in different force and speed combinations — each has a different internal gear ratio optimized for its intended application. A heavy-duty track actuator rated at 400+ lbs uses a higher gear ratio than a fast micro actuator rated for speed over force.
The lead screw adds an additional mechanical advantage on top of the gear ratio. The screw's pitch (threads per inch or mm per revolution) determines how far the rod extends per revolution of the screw. A finer pitch gives more force but slower travel; a coarser pitch gives faster travel but less force.
For a deeper look at actuator internals, see our Inside a Linear Actuator guide.
Gears Inside Rotary Actuators
A rotary actuator produces controlled rotational motion rather than linear motion. Instead of driving a lead screw, the gear train's output is the rotary output shaft itself.
Rotary actuators commonly use:
- Spur gear trains for simple, cost-effective designs
- Planetary gear trains for compact, high-torque applications (robotics, automation)
- Worm gear drives for applications that need self-locking (holding a load in position without power)
- Harmonic drives (strain wave gears) for ultra-precise positioning with zero backlash (robotics, CNC, satellite antennas)
The gear ratio in a rotary actuator determines the output torque and rotational speed, using the same formulas as any gear train. A higher ratio means more output torque at lower speed.
Idler Gears Explained
An idler gear is any gear placed between the driver and driven gear that transmits motion without changing the overall gear ratio. Idler gears serve two purposes:
- Direction change: Each additional gear mesh reverses the direction of rotation. An even number of total gears gives the same direction as the driver; an odd number reverses it.
- Bridging distance: If the driver and driven shafts are too far apart for direct meshing, idler gears bridge the gap.
The key rule: idler gears do not affect the overall gear ratio. Only the first (driver) and last (driven) gears determine the ratio. However, each gear mesh does introduce a small efficiency loss (1–3% per mesh), so adding idler gears slightly reduces total system efficiency.
Common Gear Ratios by Application
| Application | Typical Gear Ratio | Purpose |
|---|---|---|
| Bicycle (low gear) | 1:1 to 0.7:1 | Max torque for hill climbing |
| Bicycle (high gear) | 3:1 to 4:1 | Max speed on flat ground |
| Car 1st gear | 3:1 to 4.5:1 | High torque for starting |
| Car 5th/6th gear | 0.7:1 to 1:1 | Overdrive for highway cruising |
| Linear actuator (standard) | 20:1 to 80:1 | Force 50–400 lbs at 0.5–2 in/sec |
| Linear actuator (high force) | 80:1 to 150:1+ | Force 400–2000+ lbs, slow speed |
| Micro actuator (fast) | 10:1 to 30:1 | Speed over force |
| Robot joint (servo) | 50:1 to 160:1 | Precision torque control |
| Conveyor drive | 10:1 to 60:1 | Controlled belt speed |
| Winch / crane hoist | 30:1 to 300:1 | Very high torque for heavy lifting |
| Clock mechanism | Various staged ratios | Precise time division |
| Hand drill (manual) | 1:3 to 1:5 (overdrive) | Speed multiplication for fast drilling |
How to Choose the Right Gear Ratio
Selecting the correct gear ratio comes down to answering three questions:
1. What output speed do you need? If you know the motor speed and the required output speed, the ratio is: Gear Ratio = Motor RPM ÷ Required Output RPM.
2. What output torque do you need? If you know the motor torque and the required output torque, the ratio is: Gear Ratio = Required Torque ÷ (Motor Torque × Efficiency).
3. What are the physical constraints? Single-stage spur gears are limited to about 6:1 before the driven gear becomes impractically large. Planetary stages handle 3:1 to 10:1 each. Worm gears can achieve 100:1 in a single stage but at the cost of efficiency.
For actuator selection, you do not need to calculate the internal gear ratio yourself — the actuator's force rating and speed rating already reflect the gear ratio chosen by the manufacturer. Instead, focus on matching the actuator's output specifications to your application. Use our free calculators to size the right actuator.
Common Mistakes in Gear Ratio Calculations
- Confusing driver and driven: Always confirm which gear is the input (connected to the motor) and which is the output (connected to the load). Reversing them inverts the ratio.
- Counting idler gears in the ratio: Idler gears change direction, not ratio. Only the first and last gears matter for the ratio calculation.
- Forgetting efficiency: Real gears lose energy to friction. Always apply an efficiency factor (90–98% for most gear types) when calculating output torque. Ignoring efficiency overestimates the output.
- Mixing units: If torque is in N·m, keep it in N·m throughout. If in lb·in, stay in lb·in. Converting mid-calculation is a common source of error.
- Ignoring backlash: Every gear mesh has a small gap (backlash) between teeth. In precision applications, backlash introduces positioning error. Planetary and harmonic drives minimize backlash; spur gears have the most.
Related Guides and Calculators
- Linear Actuator Engineering Guide — complete reference for force, stroke, duty cycle, and sizing
- Inside a Linear Actuator — detailed technical breakdown of internal components
- Types of Electric Linear Actuators — standard, micro, track, and column comparison
- Duty Cycle Explained — thermal limits and motor protection
- IP Ratings Explained — environmental protection for outdoor and marine applications
- 5 Steps Before Buying an Actuator — avoid common purchasing mistakes
- Lid and Hatch Calculator — force and stroke sizing for hinged applications
- Linear Motion Calculator — push/pull/slide sizing tool
- Full Calculator Suite — all FIRGELLI engineering tools
- Shop Linear Actuators — browse all models by force, stroke, and speed
Frequently Asked Questions About Gear Ratios
What is gear ratio?
Gear ratio is the relationship between the number of teeth on two meshing gears. It determines how rotational speed and torque are transferred between the driving gear (input) and the driven gear (output). A gear ratio of 4:1 means the input gear must rotate 4 times for the output gear to rotate once — output speed is 4 times slower, but output torque is 4 times greater.
How do you calculate gear ratio?
Divide the number of teeth on the driven gear by the number of teeth on the driving gear: Gear Ratio = Driven Teeth ÷ Driver Teeth. For example, a 60-tooth driven gear and a 20-tooth driver gear gives 60 ÷ 20 = 3:1. For multi-stage systems, multiply the individual stage ratios together.
What is the difference between gear ratio and gear reduction?
Gear ratio is the mathematical relationship between two gears (driven teeth ÷ driver teeth). Gear reduction specifically refers to a gear ratio greater than 1:1, where the output rotates slower than the input but with more torque. All gear reductions have a gear ratio, but not all gear ratios are reductions — ratios below 1:1 are called overdrive, where output spins faster with less torque.
Does an idler gear change the gear ratio?
No. An idler gear placed between the driver and driven gear changes the direction of rotation but does not affect the overall gear ratio. The ratio depends only on the first (driver) and last (driven) gears in the train. However, each additional gear mesh does introduce a small efficiency loss (typically 1–3% per mesh).
How does gear ratio affect speed and torque?
Speed and torque are inversely related through the gear ratio. Output Speed = Input Speed ÷ Gear Ratio. Output Torque = Input Torque × Gear Ratio × Efficiency. A higher gear ratio means slower output but more torque. A lower ratio means faster output but less torque. This is why first gear in a car is slow but powerful, and top gear is fast but has less pulling force.
What gear ratio do linear actuators use?
Linear actuators typically use high gear reduction ratios, often between 20:1 and 100:1 or higher, combined with a lead screw that converts rotation to linear motion. Higher ratios produce more force but slower extension speed. Lower ratios produce faster speed but less force. FIRGELLI actuators use precision spur and planetary gear trains optimized for each actuator's force and speed rating.
What is a planetary gear system?
A planetary gear system consists of a central sun gear, multiple planet gears that orbit around it, and an outer ring gear. Planetary systems are compact, efficient (95–97% per stage), and can achieve high reduction ratios in a small package. They are widely used in actuators, robotics, and automotive transmissions because they distribute load across multiple gear meshes simultaneously.
How do I calculate gear ratio for a multi-stage gearbox?
Multiply the individual stage ratios together. For example, a three-stage gearbox with ratios of 3:1, 4:1, and 2:1 has a total ratio of 3 × 4 × 2 = 24:1. Total efficiency is also compounded: if each stage is 97% efficient, overall efficiency is 0.97 × 0.97 × 0.97 = 91.3%.
What is the most efficient type of gear?
Spur gears are the most efficient at 94–98% per mesh, followed closely by helical gears at 95–98%. Planetary gear systems achieve 95–97% per stage. Bevel gears are typically 93–97%. Worm gears are the least efficient at 40–90%, but they provide very high reduction ratios in a single stage and are inherently self-locking.
Why do actuators need gear reduction?
Electric motors spin fast (thousands of RPM) but produce relatively little torque. Actuators need to move slowly with high force. Gear reduction converts the motor's high speed and low torque into the low speed and high force required to push, pull, or lift loads. Without gear reduction, a small DC motor could never produce the hundreds of pounds of force that a linear actuator delivers.
