Set front and rear sprocket teeth and cadence to calculate cycling speed
Bike settings
Front chainring teeth F
T
Rear sprocket teeth R
T
Cadence
rpm
Wheel diameter700C (2.096m)
Rider + bike weight
kg
Power output P
W
Gear ratio 2.94
Results
Gear Ratio G
2.94
F/R
Speed v
33.3
km/h
Rollout
6.16
m/revolution
Gear inches
79.4
in
Cadence
90
rpm
Climbable gradient
3.1
%
Gear Ratio Map
Speed vs Cadence
Speed vs Cadence
Climbing Ability
Theory & Key Formulas
$$G = \frac{F}{R}, \qquad L = G\,\pi d, \qquad v = \frac{G\,\pi d\,n_{cad}}{60}$$
The gear ratio \(G\) is the front chainring tooth count \(F\) divided by the rear sprocket tooth count \(R\) (rear-wheel revolutions per pedal revolution). Rollout \(L\) is the distance traveled per pedal revolution (\(d\) = wheel diameter, \(\pi d\) = circumference in m). Speed \(v\) is proportional to cadence \(n_{cad}\) (rpm), with km/h given by \(v=L\,n_{cad}/60\times3.6\). Gear inches \(= G\cdot d_{\text{wheel}}[\mathrm{in}]\). Climb angle is \(\theta=\sin^{-1}(P/(mgv))\).
FAQ
What is cadence?
Cadence is the number of pedal revolutions per minute. Professional cyclists typically use 80-100 rpm; hill climbing often requires 60-70 rpm.
What is a typical gear ratio range for road bikes?
From high gear like 50T/11T (G=4.5) for sprinting, to low gear like 34T/32T (G=1.06) for steep climbs.
Is it more efficient to push harder gears or spin lighter ones?
Physiologically, higher cadence (~90 rpm) generally distributes muscle load better, but the optimal cadence varies by individual.
What does 700c mean?
A French wheel standard where the tire outer diameter is nominally 700 mm (actual rim diameter ~622 mm). The standard for road bikes.
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I can see the simulation updating, but what exactly is being calculated here?
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Great question! The simulator solves the governing equations in real time as you move the sliders. Each parameter you control directly affects the physical outcome you see in the graph. The key is to build an intuitive feel for how each variable influences the result โ that's how engineers develop physical judgment.
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So when I increase this parameter, the curve shifts significantly. Is that a linear relationship?
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It depends on the model. Some relationships are linear, but many engineering phenomena are nonlinear. Try moving the sliders to extreme values and see if the output changes proportionally โ if the graph shape changes, that's a sign of nonlinearity. This hands-on exploration is exactly what simulations are best for.
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Where is this kind of analysis actually used in practice?
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Constantly! Engineers run these calculations during the design phase to quickly screen parameters before investing in expensive physical tests or detailed finite element simulations. Getting comfortable with these simplified models is a real engineering skill.
