Gear Ratio Calculator
Calculate gear ratios, output speed, torque, and angular velocity for spur, bevel, or planetary gears. Step-by-step solutions with SI units included.
gear ratio calculator:
This is a Gear Ratio Calculator that allows one to compute speed, torque, and the ratio between driving and driven gears. Input speed/torque or input number of teeth. Calculations step-by-step provide velocity ratios, multiplication of torque and speed of output in spur, bevel, or planetary gear systems.
gear ratio Tool Formula:
Formula:
Gear Ratio (GR) = Number of Teeth on Output Gear / Number of Teeth on Input Gear
Output Speed = Input Speed / Gear Ratio
where GR = Gear Ratio, RPM = Revolutions per Minute
The Gear Ratio Calculator enables one to examine rotational velocity, torque, and velocity ratios in mechanical gear systems such as spur, bevel, and planetary gears. Gear ratio = the number of teeth in the driven gear/number of teeth in the driving gear:
\[ \textrm{Gear Ratio (GR)} = \frac{N_{driven}}{N_{driven}} = \frac{\omega_{driven}}{\omega_{driven}} \]
The user can either key in the number of teeth, the input speed (RPM), or the input torque, and the calculator will compute the output speed, the torque, and the gear ratio. The solution in steps displays the relationship between the output and input shafts, torque multiplication, and velocity ratios.
The tool allows the use of SI units: RPM/speed, rad/s/angular velocity, and N/m/torque. Answers to these questions can be calculated and be graphical in nature in terms of the required number of teeth per ratio, plotting speed against torque, and printable kinematic summaries are optional. It is perfect for mechanical engineers, designers, students, and hobbyists dealing with gears and transmission systems.
⚡ Work & Installation Input to Output:
Input:
- Number of teeth on driver (N_driver) and driven (N_driven) gears
- Optional: input speed (RPM or rad/s) and input torque (N·m)
- Units: RPM, rad/s, N·m
Processing:
- Compute gear ratio: GR = N_driven / N_driver
- Compute output speed: ω_driven = ω_driver / GR
- Compute output torque: T_driven = T_driver × GR
- Optional: compute planetary gear ratios using sun, planet, and ring teeth
- Validate input (non-zero teeth, positive speed and torque)
Output:
- Gear ratio (GR)
- Output speed (RPM or rad/s)
- Output torque (N·m)
- Step-by-step formulas
- Optional diagrams and printable results
Testing and Final Adjustments
Test common scenarios:
- Spur gears: N_driver = 20, N_driven = 40 → GR = 2, output speed = ω_driver / 2, torque ×2
- Bevel gears: N_driver = 15, N_driven = 45 → GR = 3, verify step-by-step solution
- Planetary gears: sun = 20, planet = 40, ring = 80 → compute compound ratio
- Edge cases: equal teeth (GR = 1), input speed 0 → output speed 0
- Validate unit conversions (RPM ↔ rad/s, torque in N·m)
- Ensure mobile/desktop UX: numeric keypad, field labels, error messages
- Include presets for automotive, industrial, and hobbyist gear systems
- Optimize SEO metadata: "Gear Ratio Calculator," "Spur Gear Speed," "Torque Calculator," "Velocity Ratio," and schema markup
Frequently Asked Questions - Gear Ratio Calculator:
What is a gear ratio?
The gear ratio is the ratio of the number of teeth on the driven gear to the driver gear or the ratio of input speed to output speed.
How do I calculate output speed?
Output speed ω_driven = ω_driver / gear ratio (GR).
How do I calculate output torque?
Output torque T_driven = T_driver × gear ratio (GR).
What units are supported?
RPM or rad/s for speed, N·m for torque, number of teeth for gears.
Can this calculator handle planetary gears?
Yes, it can compute gear ratios, speed, and torque for sun, planet, and ring gears.
Is step-by-step solution available?
Yes, all formulas and substitutions are displayed step-by-step.
Who should use this calculator?
Mechanical engineers, students, designers, and hobbyists working with gears.
Can it calculate required teeth for a desired ratio?
Yes, users can determine teeth numbers for a specific gear ratio.
Does it support torque amplification calculations?
Yes, output torque is computed based on gear ratio and input torque.
Can I convert speed units?
Yes, speed can be converted between RPM and rad/s.
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