# Grade Adjusted Pace Calculator

# Grade Adjusted Pace

## What is Grade Adjusted Pace?

Grade Adjusted Pace (GAP) is a flat-run equivalent pace based on the pace carried out over a particular gradient.

Put another way, the pace that is achieved over a hilly course is converted into a pace that would be expected if a similar effort was carried out on a completely flat course.

The calculator takes into account both the uphill and downhill components of the run, and generates a new "grade-adjusted pace" as well as a flat equivalent time.

## Using GAP

### Benefits

One benefit of grade adjusted pace is its ability to help predict an upcoming race time on a flat course based on a recent hilly run.

It's also useful in that it allows you to evaluate the performance of hilly runs and compare them to less hilly or flat runs.

### Limitations

Different runners will vary in their hill running efficiency. For example, a runner that has improved their running economy by including hilly runs in their training will be less affected by an undulating course, and heavier runners tend to slow down more when running uphill.

Terrain and steepness of slopes will also have an impact on uphill and downhill pace. The relationship between how much you slow down or speed up is fairly well correlated with the gradient unless you are dealing with very steep slopes.

The terrain and steepness of slopes will also have an impact on hilly run paces and speeds. The relationhsuipo

There are many factors unrelated to gradient that affect the overall pace of a run, such as temperature, precipitation, altitude, and fatigue levels.

The results generated by this GAP calculator should be considered in this context of these limitations.

## GAP on the web

You may see Grade Adjusted Pace used for runs on Strava or Garmin. These GAP estimates are proprietary and will differ somewhat from that used for this calculator. Especially since finer detail of undulations allows for a more-sophisticated analysis. However, all will provide a respectable estimate of your flat run equivalent.

# How It Works

The core calculation is based on research carried out by D. B. Dill, in which he determined that the cost associated with the vertical component of running uphill (i.e. the elevation gain), is 1.31 millilitres of oxygen for every metre climbed per kilogram of weight.

This value should hold true unless you're running very steep gradients. The problem with steep slopes that special effort needs to be put into maintaining running motion and the biomechanics of movement, and energy needs, become quite different.

If we take a time for a run that includes a hilly component, we can estimate the overall energy requirements for that run by calculating VO_{2} Max.

However, implicit in that calculation is the assumption that the run was completed on a flat course. So, in reality our runner will have a higher VO_{2} Max.

If we take the elevation of the run and assume the requirement of 1.31 ml of oxygen per kilogram, we can calculate the oxygen requirements for the climbing component of the run

We also consider the reduced effort needed for the downhill component of the run. Given that downhill running yields a speed increase of roughly 55% of the speed decrease suffered from uphill running, we reduce this multiple of 1.31 by 55%. We now have the overall additional oxygen requirements for the run, considering both uphill and downhill components, add that to our VO_{2}

Note that if your run was performed completely uphill, which is likely the case if it was performed on a treadmill or if you were running reps, then you can specify this with the "uphill only" checkbox.

Finally, we use this new VO_{2} Max value to carry out a reverse VO_{2} Max calculation to determine the expected time for the run distance if performed on the flat.

## Using the calculator

The fields are largely self-explanatory. However, some may require some further explanation.

### Elevation Gain

Note that this is the *total* or *cumulative* elevation gain for the run; **not** the net elevation gain (which on a loop will be zero).

### Treadmill Grade

You can enter the treadmill grade directly, or it will be automatically calculated from distance run and elevation entries, or converted from the angle entry.

Treadmill grades are usually expressed as a percentage, and thus range from 0, which is completely flat, to 100, which means the vertical component of the run matches the horizontal component of the run. E.g. if you ran 80 meters with an elevation gain of five meters, that would be equivalent to a treadmill grade of `5 / 80 × 100 = 6.25%`

.

You can convert angle to grade as follows:

```
````grade = tan(angle) × 100`

### Angle

You can enter the angle directly, or it will be automatically calculated from distance run and elevation entries, or converted from the grade entry.

Angle is measured in degrees and can range from 0, which is completely flat, to 45, which means the vertical component of the run matches the horizontal component of the run. E.g. if you ran 100 meters with an elevation gain of 100 meters, that would be equivalent to an angle of `45°`

.

You can convert grade to angle as follows:

```
````angle = arctan(grade / 100)`