Cycling Cadence & Speed Calculator
Inputs
| Solve for | Find speed |
|---|---|
| Cadence | 90 |
| Target Speed | 30 km/h |
| Chainring (teeth) | 50 |
| Sprocket (teeth) | 17 |
| Wheel Circumference | 2.11 m |
Cycling Cadence & Speed Calculator
Relate cycling cadence, gear ratio, and speed. Solve for speed, the cadence needed for a target speed, or the sprocket size needed to ride a target speed at a chosen cadence.
Inputs
Inputs
Results
Enter a value to see results.
Details
What Cycling Cadence Is — and Why It Matters
Cadence is the number of times you complete a full pedal revolution per minute (rpm). Alongside power and gear selection, cadence is one of the three levers every cyclist uses to manage effort and speed. The same speed can be achieved at wildly different cadences by choosing different gears — and that choice has measurable physiological consequences.
This calculator solves the drivetrain identity in three directions. Pick a mode and the other three drivetrain variables stay as inputs:
- Find speed — given cadence, gearing, and wheel circumference, compute ground speed.
- Find cadence — given a target speed and the gear you are in, compute the cadence you have to spin at.
- Find sprocket — given a target speed and the cadence you want to hold, compute the rear sprocket size you need on the current chainring.
How the Calculation Works
The Core Identity
Ground speed depends on three things: how fast you spin the cranks, how many times the rear wheel turns per crank revolution (gear ratio), and how far the wheel travels in one revolution (wheel circumference).
v=60cadence×sprocketchainring×CwWhere is speed in m/s, cadence is in rpm, and is wheel circumference in metres. Any one of the four unknowns (, cadence, sprocket, chainring) can be isolated by rearranging this single equation.
Gear Ratio
G=TsTcChainring teeth () divided by sprocket teeth (). A 50T chainring with a 17T sprocket gives : the rear wheel completes 2.94 revolutions per pedal stroke.
Development (Roll-out)
Multiplying gear ratio by wheel circumference gives the development — the distance covered per crank revolution:
d=G×CwA 50/17 gear on a 700c × 25 mm wheel (2105 mm circumference) develops m per pedal stroke.
The Three Modes
The calculator rearranges the same identity three ways:
Mode 0 (find speed):v=60⋅Tscadence⋅Tc⋅Cw Mode 1 (find cadence):cadence=Tc⋅Cwv⋅60⋅Ts Mode 2 (find sprocket):Ts=60⋅vTc⋅cadence⋅CwMode 2 returns a continuous number; real cassettes only have whole-toothed cogs (and only the cogs you actually own), so round to the nearest available sprocket and live with a small offset in either cadence or speed.
Cadence and Physiology
The Optimal Range
Research by Vercruyssen & Brisswalter (2010) found the metabolically efficient cadence for trained cyclists peaks around 80–100 rpm. At this range:
- Torque per stroke is moderate — not so high that it causes rapid localised muscle fatigue, not so low that neural coordination costs dominate.
- Oxygen cost is near minimum — below ~70 rpm the cardiovascular system is underutilised relative to the muscular demand; above ~110 rpm the oxygen cost of moving the legs themselves (limb inertia) rises quickly.
Beginners commonly settle at 60–70 rpm because lower cadence "feels" stronger and more controlled. With cardiovascular conditioning, most riders naturally migrate upwards.
Cadence and Power
Power = torque × angular velocity. For a fixed power output, spinning faster means less torque per stroke, which spares slow-twitch fibres and delays muscular fatigue. This is why Tour de France riders spin at 95–105 rpm in time trials even though lower cadences would feel "easier" on the legs momentarily — the sustained effort favours the cardiovascular system's greater fatigue resistance.
High-Cadence Caveats
Very high cadences (>110 rpm) come with trade-offs:
- Neural coordination cost rises — the brain and nerves work harder to coordinate rapid, precise movements.
- Cardiovascular demand spikes — heart rate rises disproportionately, which at threshold intensities can push you above your sustainable zone.
- Technique matters — at high rpm, any ankling or hip-rocking amplifies, wasting energy and increasing injury risk.
Practical Scenarios
1. Finding Your Cruise Gear (Find speed)
Plug in your typical cadence (say 90 rpm), your usual chainring, and your favourite rear sprocket. Read off the speed. If it matches your typical road speed, you've confirmed your default gear selection is well-matched to your cadence.
2. Climbing Strategy (Find sprocket)
On a 10% gradient your speed might drop to 12 km/h, but you want to hold around 75 rpm so you do not stall the cranks. Switch to Find sprocket, enter 12 km/h, 75 rpm, your inner chainring, and your wheel size. The result is the rear sprocket you need. If the answer is 28T but your cassette only goes to 25T, you are under-geared for that climb at that cadence and should either spin slower, push harder, or fit a wider cassette.
3. Time-Trial Pacing (Find cadence)
You know the speed you intend to hold on a flat time-trial course (say 40 km/h). Switch to Find cadence, enter that speed, your big-ring + small-cog combination, and your wheel circumference, and the calculator tells you the cadence that combination forces on you. If it lands above 105 rpm you'll burn out cardiovascularly; if it lands below 75 rpm you'll stress the knees. Choose the gear that lands the cadence near your sustainable sweet spot.
4. Matching Rollers or Turbo Trainer
Indoor trainers have resistance curves that depend on wheel speed. Knowing your speed from cadence and gear helps you set the correct resistance to replicate outdoor feel.
Wheel Circumference: Getting It Right
The wheel circumference value affects every speed and distance calculation. Common sources of error:
| Source | Typical Error |
|---|---|
| Using tyre size chart (inflated to spec) | ±0–10 mm |
| Tyre chart with wrong inflation pressure | ±10–30 mm |
| Nominal rim size (ignoring tyre) | ±50–150 mm |
The roll-out method (mark tyre → roll one revolution → measure) at your actual riding pressure gives the most accurate circumference and accounts for tyre deformation under rider weight. A 10 mm error in circumference translates to roughly a 0.5% error in calculated speed — negligible for most uses, but worth correcting if you are calibrating a cycle computer or comparing power meters.
Caveats
- No drivetrain losses modelled. Real drivetrains lose 1–4% of power to chain friction, flex, and bearing drag. The calculator gives theoretical ground speed; actual speed will be marginally lower for the same cadence and gear.
- Wheel circumference changes with load and pressure. A fully loaded touring bike will have a slightly larger contact patch and shorter effective circumference than the same bike unloaded at the same pressure.
- GPS vs. calculated speed. GPS-derived speed is affected by signal sampling rate and multipath error; calculated speed from cadence sensors is affected by circumference accuracy. Neither is ground truth.
- Find-sprocket results are continuous. Real cassettes only have integer-toothed cogs, and only the cogs in your spread. Round to the nearest you own and accept a small offset.
Frequently Asked Questions (FAQ)
What is the optimal cadence for cycling?
Research (Vercruyssen & Brisswalter, 2010) puts the most metabolically efficient cadence for trained cyclists at around 80–100 rpm. Beginners often gravitate to lower cadences (60–70 rpm) because they rely more on muscle force than cardiovascular endurance. Pro riders typically spin at 90–110 rpm in races to spare leg muscles on long efforts.
How do I calculate gear ratio?
Gear ratio = chainring teeth ÷ sprocket teeth. A 50-tooth chainring with a 17-tooth sprocket gives 50/17 ≈ 2.94 — the rear wheel turns 2.94 times per pedal stroke. Multiplying gear ratio by wheel circumference gives the distance covered per pedal revolution, sometimes called "development" or "roll-out".
How do I measure my wheel circumference?
The most accurate method: inflate the tyre to your usual riding pressure, place a mark on the tyre and on the ground, roll the bike forward one full revolution, and measure the distance between the two ground marks. This accounts for the actual loaded tyre profile. Alternatively, use the printed tyre size and a reference table — 700c × 25 mm is 2105 mm, 700c × 28 mm is 2136 mm.
Does a higher cadence always mean more power?
Not directly. Power = torque × angular velocity. At the same power output, a higher cadence means lower torque per pedal stroke, which reduces localised muscle fatigue and is generally easier to sustain. However, very high cadences (>110 rpm) increase cardiovascular demand and can exceed the point where efficiency gains reverse. Most riders optimise around 85–100 rpm for time-trial efforts.
Disclaimer
Speed values assume a perfectly rigid drivetrain with no slip. Real-world speeds vary with tyre deformation, chain flex, and road surface. Wheel circumference depends on tyre pressure and rider weight.