Calculator Inputs
Example Data Table
Use these sample values to compare common road cycling scenarios.
| Scenario | Cadence | Gear | Grade | Wind | CdA | Expected Use |
|---|---|---|---|---|---|---|
| Flat endurance ride | 90 rpm | 50 / 17 | 0% | 0 km/h | 0.32 | Steady aerobic pacing |
| Rolling road | 85 rpm | 50 / 19 | 3% | 5 km/h | 0.34 | Mixed terrain planning |
| Fast group ride | 100 rpm | 52 / 14 | 0% | -3 km/h | 0.28 | Aero speed estimate |
| Climbing effort | 75 rpm | 34 / 28 | 8% | 2 km/h | 0.36 | Hill power check |
Formula Used
Gear ratio: front teeth / rear teeth
Wheel circumference: π × wheel diameter
Speed from cadence: (cadence / 60) × gear ratio × wheel circumference
Cadence from speed: speed / (gear ratio × wheel circumference) × 60
Angular velocity: cadence × 2π / 60
Power from torque: torque × angular velocity
Rolling force: mass × gravity × cos(angle) × Crr
Climbing force: mass × gravity × sin(angle)
Aero force: 0.5 × air density × CdA × relative air speed²
Required crank power: ((rolling + climbing + aero force) × speed) / drivetrain efficiency
How to Use This Calculator
- Select whether you want to find speed from cadence or cadence from speed.
- Enter your chainring, rear cog, and wheel diameter.
- Add rider mass, bike mass, road grade, wind, drag area, and rolling resistance.
- Enter crank torque to compare your available torque power.
- Press the calculate button.
- Review the result box shown above the form.
- Use the chart to compare power demand at different speeds.
- Download the result as CSV or PDF for records.
Speed, Cadence, and Power in Cycling Physics
What the Calculator Measures
Speed, cadence, and power are tightly connected. Cadence tells how fast the crank turns. Gearing tells how far the wheel moves for each crank turn. Power tells how much work is delivered each second. This calculator joins those ideas in one place.
Why Cadence Matters
A higher cadence can raise speed when the gear stays fixed. Yet cadence alone does not show the full effort. A rider can spin fast in an easy gear. Another rider can push slowly in a hard gear. Both cases may create different torque and power values.
Why Power Changes Quickly
Power demand rises fast as speed increases. Air drag becomes very important at higher speeds. A small headwind can also raise the required power. Grade has a strong effect on climbs. Total mass becomes more important when the road tilts upward.
Using the Results
The result box gives road speed, cadence, power, torque, gear ratio, and ride time. The force table separates rolling, climbing, and aerodynamic resistance. This helps you see which factor controls the effort. The power curve shows how the same setup behaves across many speeds.
Practical Training Value
Cyclists can use this tool before workouts. Coaches can compare gearing choices. Commuters can estimate ride time. Indoor riders can study cadence targets. The numbers are estimates, but they give a useful physics-based guide. Better input values produce better results.
Important Limits
Real rides include turns, braking, road texture, body position changes, traffic, and fatigue. This calculator uses steady riding assumptions. It is best for planning, comparison, and education. Use measured power data when exact performance tracking is required.
FAQs
1. What is cadence in cycling?
Cadence is the number of crank revolutions per minute. It shows how quickly your legs are turning the pedals.
2. How does gearing affect speed?
A higher gear ratio moves the wheel farther for each crank turn. This can increase speed at the same cadence.
3. Why is my power estimate higher on climbs?
Climbing adds gravitational resistance. More mass and steeper grade require more power to maintain the same speed.
4. What does CdA mean?
CdA is drag coefficient multiplied by frontal area. Lower CdA usually means better aerodynamic efficiency and less air resistance.
5. Can I enter tailwind?
Yes. Enter a negative wind value for tailwind. This lowers relative air speed and reduces aerodynamic power demand.
6. What is drivetrain efficiency?
Drivetrain efficiency estimates how much crank power reaches the wheel. Losses occur through chain, gears, bearings, and alignment.
7. Is this calculator useful for running?
It is designed for cycling physics. Some resistance ideas overlap, but cadence and gearing formulas are bicycle specific.
8. Are the power results exact?
No. They are physics-based estimates. Real conditions, posture, tire pressure, surface quality, and sensor accuracy can change actual power.