Slope & Grade Calculators
Rise over run sounds simple until the units get mixed. Slope & Grade Calculators convert between percent, ratio, and degrees. Check ramps and sidewalks, find drop per foot, set elevations, and square corners with the 3-4-5 rule.
One Slope, Three Ways to Write It
Slope & Grade Calculators all start from the same idea. Slope is rise divided by run. The confusion comes from how that number gets written.
Civil plans use percent. Codes often use a ratio like 1:12. Tools and levels read in degrees. Carpenters and plumbers think in inches per foot. They all describe the same tilt.
$$\text{Percent slope} = \frac{\text{Rise}}{\text{Run}} \times 100$$
Rise and run must be in the same unit. The angle in degrees is the arctangent of rise over run.
| Percent | Ratio | Degrees | Inches per foot |
|---|---|---|---|
| 1.04% | 1:96 | 0.60° | 1/8 in |
| 2.08% | 1:48 | 1.19° | 1/4 in |
| 4.17% | 1:24 | 2.39° | 1/2 in |
| 5% | 1:20 | 2.86° | 0.6 in |
| 8.33% | 1:12 | 4.76° | 1 in |
| 10% | 1:10 | 5.71° | 1.2 in |
| 50% | 1:2 | 26.57° | 6 in |
| 100% | 1:1 | 45° | 12 in |
Percent and degrees are not the same scale. A 100% slope is only 45°. Treating one as the other is a common mistake.
Which Tool Answers Your Question
“How steep is it?”
The Slope Calculator finds slope, angle, and grade between two points. The Percent Slope Calculator works straight from rise and run. The Grade Slope Calculator converts a known grade between percent, ratio, and degrees.
“How much does it drop?”
The Slope Per Foot Calculator gives drop per foot and total fall over a run. Use it for drains, patios, and any surface that needs to shed water.
“Is it accessible?”
The Ramp Slope Calculator checks slope and length against a target ratio. The Sidewalk Slope Calculator checks both the running slope and the cross slope of a walk.
“What is the elevation?”
The Elevation Calculator Construction tool finds site elevations from a benchmark and level readings. The Elevation Grade Calculator finds the grade between two known elevations. The Vertical Curve Calculator works out elevations along a road curve that joins two grades.
“Is the corner square?”
The 3-4-5 Rule Calculator checks a right angle on site with a tape measure. It scales the 3-4-5 triangle up to the size of your layout.
ADA Ramp and Walk Limits
The 2010 ADA Standards set the slopes for accessible routes. These are the numbers most people check.
| Item | Limit |
|---|---|
| Surface counted as a ramp | Steeper than 1:20 (5%) |
| Ramp running slope, new work | 1:12 max (8.33%) |
| Ramp cross slope | 1:48 max (2.08%) |
| Rise per ramp run | 30 in max |
| Landing slope | 1:48 max |
At 1:12, every inch of rise needs a foot of ramp. A 30 inch rise needs a run of at least 30 feet. Anything higher needs a level landing between runs.
Existing buildings with tight space have limited exceptions. Local code may also add its own rules.
Measure Run the Right Way
Run is the horizontal distance. It is not the length along the sloped surface. On gentle slopes the two are close. On steep ones they drift apart.
Use a level and a straight board, a laser, or plan dimensions for run. Measure rise straight up from the low point.
Reading Elevations on Site
Site elevations usually come from a level and a rod. Start from a benchmark with a known elevation.
Add the backsight reading on the benchmark to its elevation. That gives the height of the instrument. Subtract the foresight reading at each point to get that point’s elevation.
Once you have two elevations, divide their difference by the distance between them. That is the grade.
Vertical Curves in Brief
Roads and long drives do not change grade at a sharp point. They use a parabolic curve to blend one grade into the next.
$$y = y_{PVC} + g_1 x + \frac{(g_2 – g_1)}{2L} x^2$$
Here y is the elevation at distance x from the start of the curve. The grades g₁ and g₂ are written as decimals. L is the curve length.
The high or low point matters for drainage. It falls where the grade reaches zero.
Squaring a Corner
A triangle with sides of 3, 4, and 5 always has a right angle. Measure 3 ft along one line and 4 ft along the other. If the diagonal between those marks is exactly 5 ft, the corner is square.
Larger multiples are more accurate on big layouts. Try 6-8-10 or 9-12-15. Small tape errors matter less over longer sides.
FAQs
How do I calculate percent slope?
Divide rise by run, then multiply by 100. A 2 ft rise over 40 ft of run is a 5% slope.
Is a 100% slope vertical?
No. A 100% slope rises 1 foot for every foot of run. That is a 45° angle. A vertical wall has no run, so its percent slope is undefined.
What is 1/4 inch per foot as a percent?
About 2.08%. Divide 0.25 by 12, then multiply by 100. It is the same as a 1:48 ratio.
What is the maximum ADA ramp slope?
For new construction, 1:12, or 8.33%. Each run can rise no more than 30 inches before a landing.
What is the difference between slope and grade?
In construction they usually mean the same thing. Grade is most often written as a percent. Slope may be written as a percent, a ratio, or an angle.
Does the 3-4-5 rule work in inches or meters?
Yes. Any unit works as long as all three sides use the same one.