Elevation Change Calculator

Elevation change is the vertical distance gained (or lost) over a horizontal stretch. It is the number behind the physics of climbing: road graders, ramp designers, walkers, cyclists and delivery-route planners all ask the same question — "how far up does this slope actually go?" — and the answer depends entirely on how the slope was quoted.

The two ways slopes are quoted

• Angle in degrees — the slope's inclination from horizontal. A 10° road does not look dramatic, but hold that gradient for a kilometre and the height genuinely accumulates.
• Percent grade — rise ÷ run × 100. A 10% grade rises exactly 10 metres per 100 metres of horizontal travel.

The two scales agree closely at moderate slopes — which is why so many people assume they're interchangeable — and diverge seriously as grades grow.

The formulas

Degrees:  elevation = distance × tan(angle)
Percent:  elevation = distance × (grade ÷ 100)

The tangent step is the bridge between the two: tan(10°) ≈ 0.1763, which is why a 10° slope and an 18% grade produce almost identical climbs.

Worked example

A road climbs for 100 metres horizontally at 10°:

Elevation = 100 × tan(10°) ≈ 17.6 m

The same road at an 18% grade:

Elevation = 100 × 0.18 = 18 m

Percent grade to angle, roughly

Because tan(45°) = 1, a 45° slope is a 100% grade. For gentle gradients the two units sit almost 1:1 — a 5% grade is about 2.9° — but past roughly 30° they disconnect fast, and reading one scale as the other is a serious error.

Why horizontal distance, not path length?

A 10° slope whose sloping surface measures 100 m reaches a lower peak than one whose horizontal run is 100 m — the hypotenuse is always longer than the run. Measure along the road with a measuring wheel and you overstate the climb; at 30° the overstatement approaches 15%. For accurate elevation change, always feed the level run.

Real-world uses

• Ramps and accessibility — many wheelchair-ramp rules cap the grade around 5%; this calculator turns a permitted grade and a run into the exact rise allowed.
• Cycling and hiking — sustained climbs are planned by accumulated elevation gain; routes budget their total climb.
• Road and railway engineering — grade dictates haul cost, braking requirements and locomotive power.
• Ski and recreation design — piste difficulty and slide-garden maths are grade classifications.

Checking against a GPS or altimeter

Phone GPS altitude readings bounce around by several metres, but on a sustained slope a good fix is still a useful sanity check. For a planned walk, run this calculator once per segment and sum the rises, then compare the total against your watch's elevation-gain figure: if the two disagree by more than 10–15%, one of the segments was measured badly — almost always the run, not the rise.

Common mistakes

• Measuring the sloped path length instead of the horizontal run.
• Confusing degrees with percent grade — calling a 10° slope "10 percent" and computing with the wrong scale.
• Forgetting that the tangent is unitless: the elevation comes out in whatever unit the distance was entered in.
• Expecting grade and angle to track 1:1 on steep slopes — they only do so for small angles.

For roof slopes — which use rise-per-12-inches rather than degrees or percent — see the Roof Pitch Calculator.