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Premium experiment • speed–torque exchange

COMPUTER SCIENCE & TECHNOLOGY • ENGINEERING

Gear Ratios

Change gear tooth counts and input speed to explore ideal speed and torque tradeoffs.

● INTERACTIVEGear Ratios
Gear ratio
Output RPM
Output torque
Direction

Reasoning inspector

live model state
Input gear—
Output gear—
Gear ratio—
Input speed—
Output speed—
Ideal output torque—
Speed factor—
Ideal power check—
Rotation direction—

Explore mechanical advantage

Trade rotational speed for ideal output torque by changing the ratio between two meshed gears.

LEARN WITH THE SIMULATION

Understand Gear Ratios by experimenting.

START HERE

A simple external gear pair trades rotational speed for torque according to tooth count. If the driven gear has more teeth, it turns more slowly while ideal output torque increases; if it has fewer teeth, output speed rises while torque falls. This laboratory keeps tooth ratio, input/output RPM, ideal torque and ideal power visible together so the speed,torque exchange is understood as a consequence of kinematics plus energy conservation rather than as two unrelated formulas.

BUILD THE IDEA

What you should understand first

  • Calculate gear ratio from driven teeth divided by driving teeth.
  • Derive output speed as input RPM divided by the gear ratio.
  • Relate ideal output torque to input torque multiplied by ratio.
  • Explain why two external meshing gears reverse rotation direction and why ideal power remains unchanged.

TRY IT YOURSELF

How can a gearbox multiply torque without creating extra ideal power?

  1. Set the output gear to three times the input tooth count and record speed and torque factors.
  2. Compare input and output ideal power in the inspector.
  3. Reverse the size relationship so the output gear is smaller.
  4. Observe speed multiplication and torque reduction while ideal power remains equal in the lossless model.
Read the visual:

Gear teeth constrain tangential motion at the mesh. A reduction lowers angular speed in inverse proportion to ratio and raises torque by the same ratio, causing torque×angular-speed power to remain constant ideally.

WHY IT WORKS 01

Equal tooth-passing rate produces the inverse speed relationship

At the mesh, each gear advances through the same number of tooth contacts per unit time. A gear with more teeth therefore needs fewer complete revolutions to present the same number of teeth. This gives ωout/ωin = Nin/Nout, or output RPM equal to input RPM divided by the ratio Nout/Nin.

WHY IT WORKS 02

Ideal torque changes inversely to speed because power is conserved

For lossless steady rotation, mechanical power P=τω is the same through the gear mesh. If output angular speed is reduced by a factor r, torque must rise by the same factor r to keep the product unchanged. The inspector performs this power check using a fixed modeled input torque.

WHY IT WORKS 03

Direction reversal is separate from ratio magnitude

Two externally meshing gears rotate in opposite directions regardless of whether the ratio is a reduction, 1:1 or an overdrive. Adding an idler gear can reverse direction again without changing the magnitude of the overall ratio when its tooth count cancels from the ratio calculation.

DO NOT MIX THESE UP

Common misconception

Gear ratio is not efficiency and a gearbox cannot create energy. Real gears lose power through friction, deformation and lubrication losses. Tooth ratio also does not by itself specify maximum tooth stress, backlash or whether a chosen tooth count is mechanically practical.

PRACTICE CHALLENGE

Can you predict output speed and torque from tooth counts before changing the simulator?

  • Choose input and output tooth counts and calculate the ratio Nout/Nin.
  • Predict output RPM from inputRPM/ratio.
  • Predict ideal output torque from input torque×ratio.
  • Verify both predictions and use the power metric to explain why torque gain is paired with speed loss.
Reveal the reasoning

For one ideal external gear pair, ratio r=Nout/Nin, ωout=ωin/r and τout=τin r. Multiplying output torque by output angular speed gives the same ideal mechanical power as the input. External gears also reverse rotation direction at the mesh.

MODEL BOUNDARIES

What this simulation assumes

Every simulation simplifies reality or a mathematical system. These are the assumptions and limits to keep in mind while interpreting the results.

Model assumptions

  • Two ideal external gears mesh without slip.
  • Speed ratio is set by tooth counts, and torque scales inversely with speed in an ideal lossless transfer.
  • Gear teeth are assumed rigid and perfectly formed.

Model limitations

  • Friction, backlash, tooth deformation, inertia and efficiency losses are ignored.
  • The model does not cover compound gear trains, planetary systems or strength limits.

CONNECT IT

Where this matters

  • Vehicle transmissions
  • Robot drivetrains
  • Clocks and machinery
  • Motor speed and torque matching

WORDS THAT MATTER

Key vocabulary

Gear ratio
For this pair, driven/output tooth count divided by driving/input tooth count.
Reduction
Ratio greater than one that lowers output speed and raises ideal torque.
Overdrive
Ratio below one that raises output speed and lowers ideal torque.
Torque
Rotational moment of force, measured in newton-metres.
Mechanical power
Rate of rotational work P=τω.