Sports
Cycling Power Pace Estimator
Estimate power-scaled speed, adjusted route speed, moving time, pace, and mechanical work from an observed power-speed reference.
Cube-root power scaling factor-
Power-scaled flat speed reference-
Entered grade speed adjustment-
Speed after entered grade adjustment-
Speed after wind adjustment-
Estimated moving time (hours)-
Estimated pace (minutes/km)-
Mechanical work across estimated time-
Decision view
Cube-root cycling power-speed curve
Cube-root cycling power-speed curveA function curve shows reference power, flat target speed, and the route-adjusted speed after grade and wind inputs.
Exact scenario comparisonTarget power (W) changes while all other entered assumptions remain constant.
| Target power (W) | Cube-root power scaling factor | Power-scaled flat speed reference | Entered grade speed adjustment | Speed after entered grade adjustment | Speed after wind adjustment | Estimated moving time (hours) | Estimated pace (minutes/km) | Mechanical work across estimated time |
|---|
How to use Cycling Power Pace Estimator
- Enter a known reference power and speed.
- Enter the target power, route grade, wind adjustment, and distance.
- Use the curve and final marker to compare flat speed, adjusted speed, time, and work.
Calculator guide
Understanding Cycling Power Pace Estimator
Cycling speed does not rise linearly with power, so this estimator starts with a cube-root power curve and then applies the entered grade and wind assumptions.
Calculation method
How the calculation works
Scale speed from an observed power-speed reference using a cube-root relationship, then apply explicit grade and wind adjustment assumptions. Divide target power by reference power, take the cube root to scale speed, then apply the explicit grade and headwind speed adjustments before calculating time and work.
Detailed calculation process
Scale cycling speed from power, grade, and wind inputs
The default compares 280 W against a 220 W reference at 32 km/h, applies a 1.5% grade with a 3% speed penalty per grade point, then applies a -5% wind adjustment over 80 km.
General formula: s = (P_t/P_r)^(1/3)v_flat = v_r sg_adj = G pv_grade = v_flat(1-g_adj/100)v = v_grade(1+w/100)t = d/vpace = 60/vW_kJ = P_t t 3600 / 1000 The cube-root term models the common aerodynamic idea that power rises roughly with speed cubed. The calculator then applies the user-entered grade and wind adjustments as transparent speed multipliers.
What each symbol means
Worked substitution with the default inputs
The default modeled speed is 31.462 km/h, giving 2.543 hours of moving time and about 2,563 kJ of mechanical work.
Purpose-built visual
Power-speed function curve
The plot shows the cube-root power curve, the flat target point, and the lower route-adjusted speed point.
Worked situations
Practical examples
- The default compares 280 W against a 220 W reference at 32 km/h, applies a 1.5% grade with a 3% speed penalty per grade point, then applies a -5% wind adjustment over 80 km.
- The default modeled speed is 31.462 km/h, giving 2.543 hours of moving time and about 2,563 kJ of mechanical work.
Better inputs
Useful tips
- Use a reference power and speed recorded on the same bike, riding position, and broadly comparable surface.
- Change grade and wind separately so their explicit speed penalties are not mistaken for a power-curve effect.
- Keep power in watts, speed in km/h, distance in kilometers, and remember that mechanical work is not food calories.
Before relying on the result
Limitations and common mistakes
- This is a simplified pace estimator, not a full cycling physics solver.
- Mass, drag coefficient, rolling resistance, drivetrain loss, altitude, drafting, braking, turns, and stops are excluded.
- The grade and wind effects are user-entered planning adjustments.
Reference
Key terms
- Cube-root scaling
- A simplified way to translate a power ratio into a speed ratio.
- Modeled speed
- The final speed after power, grade, and wind adjustments.
- Mechanical work
- Power multiplied by time, converted from joules to kilojoules.
Important note
Calculated from the entered performance values using the displayed method. Health, fitness, terrain, weather, equipment, and event conditions can change real-world outcomes.
Frequently asked questions
Why does speed use a cube root?
At cycling speeds, aerodynamic demand often dominates, and aerodynamic power is roughly proportional to speed cubed.
Does the grade penalty come from physics?
No. It is the explicit planning penalty entered by the user.
Why can wind adjustment be negative?
A negative value represents a headwind or other speed-reducing condition.
Is mechanical work the same as calories burned?
No. Human metabolic energy is higher because body efficiency is limited.