Elevation Grade Calculator

Elevation Grade Calculator finds the percent grade between two elevations, or from rise and run. It also gives the slope angle, the ratio, the slope distance and the rise per foot.

Three Ways to Use the Elevation Grade Calculator

The Elevation Grade Calculator starts from whatever you have measured. Two Elevations and Distance suits survey shots, contour maps and GPS readings. Rise and Run suits a height and a length taken on site. Start Elevation and Grade works the other way and returns the elevation at the far end.

Elevation and distance do not have to share a unit. You can enter a climb in feet over a distance in miles, or a rise in inches over a run in feet. With the default entries, a rise from 100 ft to 112 ft over 300 ft is a 4.00% uphill grade.

The cards in the Elevation Grade Calculator restate that grade in the forms used on a job. They give the angle and ratio, the length along the slope, the rise per foot with a level check, and a comparison with a target grade you choose.

Elevation Grade Formula

Grade is the elevation change divided by the horizontal run, written as a percent. Subtract the start elevation from the end elevation to get the rise. A negative answer means the ground falls, and the result is labeled downhill.

$$Grade=\frac{E_2-E_1}{Run}\times 100$$

For the default example the rise is 112 minus 100, or 12 ft. Dividing 12 by 300 gives 0.04, which is 4%. The same slope is a ratio of 1 to 25, because the ground rises 1 ft for every 25 ft of run.

The angle comes from the arctangent of the grade as a decimal. It is not the grade multiplied by a fixed number. That shortcut is close on gentle slopes and badly wrong on steep ones.

$$Angle=\arctan \left(\frac{Grade}{100}\right)$$

A 4% grade is 2.29°. A 100% grade is 45°, not 57°, which is what the multiplying shortcut would give. The Elevation Grade Calculator uses the arctangent at every grade, so the angle stays right on steep ground.

Grade Elevation Conversion Chart

The chart below converts common grades to an angle, a ratio, inches of rise per foot and feet of climb per mile. The Elevation Grade Calculator builds the same chart under Grade Chart and adds a row for your own result.

Rise per foot is the grade times 0.12, and climb per mile is the grade times 52.8. To convert a ratio or an angle that is not in the chart, the Grade Slope Calculator moves between percent, ratio and degrees.

Map Distance or Slope Distance

The formula needs the horizontal run. A distance scaled from a map or a plan is already horizontal. A distance from a measuring wheel, a tape laid on the ground or a GPS track is measured along the slope, and it is always longer.

Open Distance Type and Target Grade and set Distance Was Measured to Along the slope. The Elevation Grade Calculator then finds the true run before it works out the grade.

$$Run=\sqrt{S^2-Ris{e}^2}$$

S is the distance along the slope. On gentle ground the correction is tiny. A 12 ft rise over 300 ft of slope distance gives a run of 299.76 ft and a grade of 4.00%. On steep ground it matters. A 30 ft rise over 100 ft of slope distance is a 31.45% grade, not 30%.

The second card shows the reverse figure. For a horizontal entry it gives the slope distance and a slope length factor. Multiply any plan length by that factor to order pipe, fence or paving that follows the ground. The factor is 1.0008 at 4% and 1.044 at 30%.

Finding an End Elevation From a Grade

Choose Start Elevation and Grade in the Elevation Grade Calculator when the slope is fixed and you need the elevation at the other end. Enter the start elevation, the grade and the distance. Put a minus sign on the grade for ground that falls.

$$E_2=E_1+\frac{Grade\times Run}{100}$$

From 100 ft at a 3% grade, a point 300 ft away sits at 109.00 ft. At minus 3% it sits at 91.00 ft. This is the calculation for setting a pipe invert, a swale or the far end of a driveway from one known point. Where two grades meet on a road, the Vertical Curve Calculator finds the elevations along the curve that joins them.

Checking Grade With a Level

The third card in the Elevation Grade Calculator turns the grade into numbers you can set out. A 4% grade is 0.48 in of rise per foot. Hold a 4 ft level flat on the slope and the gap under its low end is 1.92 in. In metric units the card switches to millimeters per meter and a 1.2 m level.

The same card gives the climb per mile, which is 211.2 ft at 4%. For drainage work that is specified in inches per foot, the Slope Per Foot Calculator works from the drop per foot to the total fall.

Comparing a Grade With a Target

The last card in the Elevation Grade Calculator checks your grade against a limit you set. The presets include the three slopes in the ADA Standards. A walking surface can be no steeper than 1:20, or 5%. A ramp run can be no steeper than 1:12, or 8.33%. Cross slope can be no steeper than 1:48, or 2.08%.

The card also shows what would meet the target. A 12 ft rise needs 144 ft of run at 8.33%. Over the 300 ft in the example, the most rise that still meets 8.33% is 25 ft. When the grade is over the target, the card is flagged and the notice below states both figures.

Grade is only one of the ramp rules. The Access Board ramp guide limits each run to 30 in of rise and requires level landings between runs. A 12 ft rise therefore takes five runs plus landings, not one 144 ft slope. The Ramp Slope Calculator and the Sidewalk Slope Calculator cover those cases.

Elevation Grade FAQ

Is 45 degrees a 50% slope?

No. A 45° slope is a 100% grade, because the rise equals the run. A 50% grade is 26.57°. Percent and degrees are close to proportional only on gentle slopes, where 1% is about 0.57°.

The gap grows with steepness. A 20% grade is 11.31°, a 30% grade is 16.70° and a 200% grade is 63.43°. A vertical wall has no percent grade at all, since the run is zero.

How steep is a 20% grade hill?

A 20% grade rises 1 ft for every 5 ft of run, at an angle of 11.31°. That is 2.4 in per foot and 1,056 ft of climb per mile. It is four times the 5% limit for an accessible walkway.

To check a hill from a map, read the two contour elevations and scale the distance between them. Enter those in the Elevation Grade Calculator with the distance left as horizontal. A 100 ft climb over 500 ft of map distance is 20%.

How do I find the elevation grade of a running route?

Use Rise and Run with the climb in feet and the distance in miles. A route that gains 500 ft over 2 miles has an average grade of 4.73%. A treadmill set to 1% matches 52.8 ft of climb per mile.

A watch or phone records distance along the ground. On most routes the difference from horizontal distance is under 1%. On a steep trail, set the distance to Along the slope so the Elevation Grade Calculator corrects for it.