What is Gear Ratio?
Gears transmit rotational motion and torque between shafts, and the gear ratio tells you exactly how speed and torque change as power flows from one gear to the next. It's the key number behind car transmissions, bicycle gearing, and clock mechanisms.
The gear ratio is GR = N₂/N₁, the driven gear's teeth divided by the driver gear's teeth. A ratio greater than 1 reduces speed and multiplies torque; a ratio less than 1 increases speed and reduces torque.
- 1↓Input shaft turns the driver gearMotor or pedal power spins the driver gear at ω_in.
- 2↓Teeth mesh and transfer motionEach tooth of the driver pushes a tooth of the driven gear.
- 3↓Driven gear rotates at a new speedSpeed scales inversely with the teeth ratio N₂/N₁.
- 4Torque changes inversely to speedIf speed drops, torque rises by roughly the same factor.
Try it: interactive calculator
Step-by-step worked examples
A driver gear with 20 teeth spins at 1200 rpm. The driven gear has 60 teeth. Find the output speed.
GR = N₂/N₁ = 60/20 = 3 ω_out = ω_in/GR = 1200/3 = 400 rpm
A bicycle chainring (driver) has 44 teeth and the rear cog (driven) has 11 teeth. Find the gear ratio and its effect on speed.
GR = N₂/N₁ = 11/44 = 0.25 ω_out = ω_in/GR = ω_in × 4 → the rear wheel spins 4 times faster than the pedals
A gear train needs a 5:1 speed reduction and the driver gear has 12 teeth. How many teeth should the driven gear have?
GR = N₂/N₁ = 5 N₂ = 5 × N₁ = 5 × 12 = 60 teeth
Flashcards
Quick quiz
Q1.If the driver gear has 15 teeth and the driven gear has 45 teeth, what is the gear ratio?
Q2.A gear ratio greater than 1 means the output gear...
Q3.In a bicycle, shifting to a smaller rear cog while keeping the same chainring...
Q4.Two meshing external gears always rotate...
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Common mistakes
Assuming gear ratio always refers to a speed increase. — Correct: A ratio greater than 1 (more driven teeth) reduces speed and increases torque; a ratio less than 1 does the opposite.
Confusing which gear is the 'driver' and which is the 'driven' gear. — Correct: The driver gear is connected to the input power source; the driven gear is turned by it.
Ignoring that torque and speed trade off inversely. — Correct: Ideally power is conserved: as speed drops, torque rises by the same factor, minus friction losses.
Believing gear ratio depends directly on gear diameter rather than tooth count. — Correct: Tooth count is proportional to radius for gears of the same module, but the ratio is defined by teeth counts, not raw diameter.
FAQ
What is the gear ratio formula?
GR = N₂/N₁, the number of teeth on the driven gear divided by the number of teeth on the driver gear.
How do you calculate gear ratio from rpm?
GR = ω_input/ω_output (input speed divided by output speed) — equivalent to the teeth ratio for ideal meshing gears.
What are examples of gear ratios in real machines?
A car's first gear (roughly 3:1 to 4:1) for torque, a bicycle's high gear (below 1:1) for speed, and a clock's gear train stepping seconds down to hours.
What does a 4:1 gear ratio mean?
The driven gear has 4 times as many teeth as the driver, so it turns 4 times slower but delivers about 4 times the torque.