Gear Ratio & Spur Gear Calculator
Gear ratio is the driven gear tooth count divided by the drive gear tooth count. A higher ratio increases torque and decreases rotational speed. Useful for automotive, motorcycle, and industrial power transmission design.
Calculate gear ratio, pitch circle diameter, center distance, tangential force, radial force (bearing load), and pitch line velocity for spur gears.
Force Analysis (Optional)
※ Enter input torque to enable force analysis
How to Use the Gear Ratio & Spur Gear Calculator
- Enter the number of teeth for the drive gear and driven gear.
- Optionally enter the module to calculate pitch circle diameters and center distance.
- Optionally enter input torque and pressure angle in the Force Analysis section to calculate tangential force, radial force, and pitch line velocity.
- Click 'Calculate' to see the results.
What Is Gear Ratio?
Gear ratio is the ratio of teeth between the driving gear and the driven gear, calculated as driven teeth ÷ drive teeth. For example, if the drive gear has 20 teeth and the driven gear has 60 teeth, the gear ratio is 3.0 (3:1).
The gear ratio determines the conversion ratio between torque and rotational speed. With a gear ratio of 3.0, the output speed is reduced to one-third of the input, while the torque is theoretically tripled. This torque amplification effect is a fundamental metric in reducer (gearbox) design.
Conversely, when the gear ratio is less than 1.0 (drive teeth > driven teeth), the assembly acts as a speed increaser, where rotational speed rises while torque decreases. Selecting the appropriate gear ratio is a key aspect of mechanical design.
Understanding Design Parameters
In addition to tooth count, 'module (m)' and 'pressure angle (φ)' are important parameters in spur gear design.
- Module（m）
- Module (m) is the reference value representing tooth size, defined as pitch circle diameter ÷ number of teeth. The JIS B 1701 standard defines preferred values such as 0.5, 1, 1.5, 2, 3, 4, 5, 6, 8, 10, etc. Meshing gears must have the same module. A larger module means larger teeth capable of transmitting greater forces.
- Pressure Angle（φ）
- Pressure angle (φ) is the inclination angle of the tooth flank. The JIS/ISO standard is 20°. A value of 14.5° comes from older standards, while 25° is used for high-strength applications. A larger pressure angle increases tooth root strength but also raises the radial force (bearing load).
Pitch circle diameter (d = m × z) is the diameter of the reference circle. Center distance (a = m(z₁+z₂)/2) is the shaft-to-shaft distance between two meshing gears, directly used in mechanical layout design.
Common Applications of Spur Gears
Spur gears are the simplest type of gear and are used across a wide range of machinery.
- Industrial Reducers
- Mounted on servo or electric motor output shafts to convert high-speed, low-torque output into low-speed, high-torque output. Used in industrial robot arm joints and conveyor drive systems.
- 3D Printers & CNC Machines
- FDM 3D printer extruders and CNC feed axes commonly use spur gears to amplify stepper motor torque while achieving precise positioning.
- Clocks & Measuring Instruments
- The wheel train of a mechanical clock is made up of multiple spur gears and crown gears, converting mainspring energy into the rotation of the second, minute, and hour hands.
Frequently Asked Questions (FAQ)
- What does a gear ratio of 1.0 mean?
- A gear ratio of 1.0 means the drive and driven gears have the same number of teeth. Neither rotational speed nor torque changes. It is used as a 1:1 direct-drive transmission.
- Can gears with different modules mesh together?
- In principle, no. Different modules mean different tooth pitches, preventing proper meshing and causing damage. Exceptions exist with specially designed profile-shifted gears.
- Why is the standard pressure angle 20°?
- The JIS/ISO standard is 20°. Compared to 14.5°, it offers greater tooth root strength and reduces the risk of undercutting. Today, 20° is used for virtually all general-purpose gears. 25° is reserved for applications requiring extra strength.
- What is the difference between tangential force and radial force?
- Tangential force (Ft) acts tangent to the pitch circle and is the primary force transmitting rotation. Radial force (Fr) acts toward the gear axis and is the load on the bearings. The relationship is Fr = Ft × tan(φ), so a larger pressure angle results in higher radial force.
- Can a large gear ratio be achieved in a single stage?
- A single gear pair has practical limits (typically up to about 1:10). For large ratios, a multi-stage gear train is used, where multiple gear pairs are arranged in series. The total gear ratio is the product of each stage's ratio.
Torque, Power & RPM Calculator
After determining the torque multiplier from the gear ratio, the actual torque, power, and RPM relationship can also be calculated. Use it when specifying motor or reducer output.