How to use the cycling climb speed calculator
- Choose whether to find the speed from your power or the power needed for a speed, and kilograms with km/h or pounds with mph.
- Enter the power (or speed), the total weight of rider, bike and gear, and the grade of the road. A grade of 7 means 7 meters up for every 100 meters along the ground.
- Add the climb length if you want the time and the height gained. Open More options for rolling resistance, drag area, air density, drivetrain efficiency and a headwind. All defaults are examples.
- Read the speed, time per kilometer or mile, power per kilogram and the split of effort between gravity, rolling and air. The last table holds your power on other grades.
Formula
force = m g (sin(angle) + Crr cos(angle)) + 0.5 rho CdA (v + headwind)^2
wheel power = v x force and pedal power = wheel power / efficiency
angle = atan(grade / 100), g = 9.80665 m/s^2
There is no closed form for the speed, so the page finds it by halving an interval until the power equation matches. The result is then put back into the equation to check it. Crr is the rolling resistance coefficient, rho the air density and CdA the drag area.
250 watts up a 7% grade
For a total weight of 78 kg, 250 W at the pedals, Crr 0.005, CdA 0.35 m^2, air density 1.2 kg/m^3 and 97% efficiency, the speed is 14.41 km/h, or 4:10 per kilometer, with 3.21 W/kg. The climbing rate is 1,006 meters per hour.
The forces at that speed are 53.4 N from gravity (88.2% of the total), 3.8 N from rolling (6.3%) and 3.4 N from air (5.6%). Holding 14 km/h takes 242 W. The same 250 W gives 35.7 km/h on the flat, 21.0 km/h at 4%, 12.9 km/h at 8% and 9.1 km/h at 12%. A 10 km/h headwind at 3% leaves 20.7 km/h, and a 5 km climb at 7% takes 20:49 and gains 349 meters.
Why climbing is mostly about weight
On steep grades gravity is nearly all of the resistance, so speed is close to proportional to power per kilogram. At low speed air drag is small, which is why the air share above is only about 6%. On flat roads the balance is reversed: air resistance grows with the square of speed and dominates.
That is why two riders with the same power can differ a lot uphill and much less on the flat, and why dropping a kilogram of bike or gear helps more on climbs. The wind row matters most at higher speeds.
Limits of a steady-state estimate
The model assumes a constant speed and a constant grade. It ignores acceleration, changing grade, riding out of the saddle, drafting and a wheel that slips. Rolling resistance and drag area depend on tires, road surface and body position, so change them to match your case. For the ratio of power to body weight and a simple climb estimate, see the Watts per Kilogram Calculator, and for training zones the Cycling Power Zones Calculator.
More hobby and sport tools
For other hobbies, sports and music, try the Darts Checkout Calculator, Lap Time Analyzer and Equivalent Exposure Calculator.
Assumptions and limits
- The speed and grade are constant, and the road is straight.
- Rolling resistance, drag area, air density and efficiency are the values you enter; the defaults are examples.
- A headwind is the speed of the air against you. Tailwinds are not modeled.
- Power is the average at the pedals. This is an estimate for planning and not a coaching or health measure.
Frequently asked questions
What is VAM?
VAM stands for vertical ascent meters per hour. It is the speed at which you climb in height, and the page shows it as the climbing rate: speed times the sine of the road angle.
Why does the model ignore tailwinds?
With a strong tailwind the power curve is no longer a single rising line, so more than one speed could match one power. Only headwinds and calm air are allowed.
Which numbers should I change first?
The weight, the grade and the power matter most uphill. Drag area and air density matter more on flat roads. Rolling resistance changes the answer a little everywhere.
How accurate is the estimate?
It is as accurate as your inputs. Small errors in the grade or weight change the result noticeably on a steep climb, so use a measured grade where you can.