# Rating Climb Difficulty

### Why rate climb difficulty?

Climb difficulty is a subjective number derived from features possessed by all climbs. Its primary purpose is to facilitate comparison of different climbs against each other, and is often found in sites seeking to map cyclists to cycling tours. Unlike elevation gain or cycling distance, climb difficulty is not a hard number, but understanding how various formulas estimate it, can provide insights as to what you are up against in attempting a ride.

### Measuring the difficulty of a cycling climb?

Many factors can make a climb difficult.  Certainly, elevation gain and cycling distance are two. But what about Summit altitude and the average riding elevation. Here the thinness of the air may also be a factor.

Physics may tell you the total work to climb to a summit is the same no matter what the route, but extremely steep ascents as oppose to gradual ascents require different power expenditures. There are local climbs in the Santa Monica Mountains that are easier to accomplish one way than another.

Finally, what about steep segments within a climb. While Physics says you will expend the same amount no matter what the route, this is hiding the fact that high expenditures are added to downhills which show up as negative effort.

There is no single formula recognized as “correct.” Each reflects a subjective factoring in of some or all of the above factors. Here are several in use today. Specific examples are provided in the Scenarios section of this website.

### ClimbByBike Formula

ClimbByBike is a website that has extensively rated hundreds of cycling climbs worldwide. The following is based on their particular formula explained on their  ClimbByBike website page.

Their formula uses three physical parameters as input: cycle distance, elevation gain, and summit elevation.

DR = (H*100/D)*2 + H²/D + D/1000 + (T-1000)/100

Whereby: H = difference in height; D = distance in meters; T = top of mountain in meters. (The last part of the formula does only apply to mountains above 1000 meters.)

You do not see any slope information such as average grade, but it is there, only implicitly. Think of the hill as a right triangle. Cycling Distance and elevation gain are two of the three sides. For a given elevation gain, the steeper the slope, the shorter the cycling distance. So ratios involving H and D do incorporate average grade.

### Gabriele Codifava Formula

An approach that explicitly factors in segment slopes has been developed by Gabriele Codifava. His approach computes difficulty using the segmented route to the summit. His notation uses the following terms:

Route Parameters:
d – total difference in altitude (meters)
P – avg. gradient expressed as Percentage (%)
L – entire Length of the climb (Km)

Segment Parameters:
li – length of the i-th interval of the climb (Km)
di – Altitude difference of the i-th interval of the climb (Km)
pi – gradient of the i-th interval of the climb (%)

Then, for each segment, he computes a weighted version giving emphasis for steep slopes, and sums the results. (Note his final result does not include di)
DInt = S [ li*pi^2/10 + 4*(pi/P)*(li/L)*pi ]
D = Sum(DInt)
Note that this formula does not include a factor for riding at high altitudes.

### Examples

In our Scenarios section, we examine a number of climbing scenarios such as the Alpe d’Huze and the Mana Lei. Examples of these difficulty calculations are provided there. In order to compute the segmented formula, we will need to gather the segmented information.

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