Bicycle Speed & Power Calculator: Recumbents, recumbent bicycles, racing bicycles, normal bicycles, aerodynamics, air drag, rolling friction, uphill power. BMI calculator.

Pictures Speed&Power Cadence SteeringGeometry SpokeLength PedalKickBack Suspension Links

Anglo-american units
metric units

Miles-to-km (or vice versa) calculator 

Racing Bicycles Recumbents
Roadster hands on the tops
(top of handlebar)
under seat steering,
commuting equipped
hands on the drops
(bottom of handlebar)
under seat steering,
commuting equipped
with racing bars
Triathlon Bicycle ShortWheelBase
above seat steering,
racing equipped

Superman Position
(Racing Bicycle-
1h Record)
above seat steering
Kreuzotter race

Lowracer with
streamlining tailbox
Kreuzotter race

Streamlined Lowracer
White Hawk
(1h World Record)

Streamlined Trike
The comma as well as the point
may be used as decimal point.
Rider's Height in / cm
Rider's Weight lb / kg
Bicycle Weight lb / kg
Air Temperature °F / °C
Height above SeaLevel ft / m
Slope of Road %
uphill positive, downhill negative values
Wind Speed mph / km/h
headwind positive, tailwind negative values
Pedaling Cadence /min
"Change" the sort of tires?
(Recumbents: calculation is based
on 20inch front wheels.)
Front Wheel Tire Rear Wheel Tire
The input field of the variable to be calculated must be empty. The result will appear in that field.
With both fields filled, the variable evaluated previously will be calculated again (facilitates quick comparisons).
Power =Watts  
Speed =mph / km/h
Further result: Effective Drag Area (Cw * A) =square feet
In case you enter (before clicking the "Calculate"-Button):
either the TripDistance miles / km ft / m
or the TripDuration h min sek,
the amount of Calories Burned by the Rider =kcal   (assumed efficiency: 25 percent) will be calculated.
Besides, the program will evaluate the variable whose fields are empty (Trip Distance or Trip Duration, respectively).

Even coast-down simulations are possible: set the Power value to zero and the Slope to the desired negative value.

TopOfPage | Speed&Power | BodyMassIndex-Calculator | Text | Formulae


About the Speed&Power Calculator:

The rider's frontal area is evaluated approximately by use of the rider's body height and body weight values, and a parameter which depends from the selected kind of bicycle (see FAQ). Inside the fully streamlined bicycles, the rider's frontal area isn't assumed to have any influence.
The rolling friction values of the front- and rear wheel tires are calculated separately.
The calculation also regards the following parameters:
load distribution front/rear wheel; a wider tire generates less rolling friction (at given inside pressure) but more air resistance (not true with the streamliners White Hawk and Quest whose fairings enclose the wheels almost completely); a thicker tire wall (touring tire) tends to generate higher rolling friction; thread induces air vortices and thus speed-dependent additional resistance; the front wheel has more share in the air drag than the rear wheel; smaller front wheels of recumbents: more rolling- but less air-friction. Even the air drag share of the bicycle by itself is taken into account.
At low speeds a wider tire (less rolling friction) may be advantageous while, with accelerated velocity, a narrower one increasingly gets the upper hand (less air friction).
The calculated rolling resistances refer to asphalt road pavement. On a smooth (wooden) velodrome surface rolling resistances may be essentially lower.
The data for the bicycles are essentially based on measurements, done with SRM Power Measuring cranks, and partly on coast-downhill comparisons.
TopOfPage | Speed&Power | BodyMassIndex-Calculator | Text | Formulae


The most essential of the formulae the Speed&Power Calculator is based on:

The following equations include any of the relevant drag components: rolling resistance, air drag (including wind speed), mechanical losses, and uphill or downhill power.
P Rider's power
V Velocity of the bicycle
W Wind speed
T Air temperature (reduced to deg. Kelvin) (influences air density)
HNN Height above sea level (influences air density)
rho Air density
rho_0 Air density on sea level at 0° Celsius (32°F)
P_0 Air pressure on sea level at 0° Celsius (32°F)
m Mass of the bicycle (influences rolling friction, slope-dependent pull-down force, and normal force)
M Mass of the rider (influences rolling friction, pull-down force, and the rider's frontal area via body volume)
A Total frontal area (bicycle + rider)
Cw Air resistance coefficient
g Gravitational acceleration
Cr Rolling resistance coefficient
Cm Coefficient for transmission losses and losses caused by tire slippage (the latter can be heard during powerful pedal strokes at low speeds, for instance by their echo when you're riding along a vertical wall)
stg Inclination (grade) of road (unit: percent)

rho = rho_0 * (273/T) * e-rho_0*g*HNN/P_0 (air density via barometric formula)
Equation for rolling friction force and pull-down force (pull-down force, normal-force-dependent rolling friction force on inclined plane (uphill or downhill))

Equation for the required human power
Solving for V:

if a2 + b3 > 0 if a2 + b3 < 0
(casus irreducibilis; happens with sufficient downhill slope or tail wind speed)
Velocity equation
Velocity equation (casus irreducibilis)

with: Expression "a" of the velocity equation and Expression "b" of the velocity equation
TopOfPage | Speed&Power | BodyMassIndex-Calculator | Text | Formulae


Relation between Body Weight, Body Height and BodyMassIndex (BMI)

The comma as well as the point may be used as decimal point.
The field of the variable to be calculated must be empty. The result will appear there.
Body Weight = lb / kg  Body Height = in / cm BMI =
Note:   BMI = weight[kg] / (height[m] * height[m])
BMI<19 signifies underweight,  BMI between 25 and 30 slight overweight...

With the values from this BMI-Calculator you can check how much any change of body weight or height (or both) would influence the bicycle speed or the required "human power". It is "fair" to compare riders with different heights at identical BMI values, meaning "adequately" changed body weights. It may become noticeable that even on a recumbent bicycle the rider's tallness has influence on air drag. A change of the rider's weight (meaning changed body surface area and thus frontal area) has more influence on aerodynamics than a different tallness alone.

TopOfPage | Speed&Power | BodyMassIndex-Calculator | Text | Formulae

Pictures Speed&Power Cadence SteeringGeometry SpokeLength PedalKickBack Suspension Links


Last modified: 26. 9. 2002

Walter Zorn