Elevation Grade Calculator
A 2-foot vertical change over 40 feet of horizontal run is a 5.0% grade, a 1:20 ratio, and a 2.9-degree angle. This elevation grade calculator converts a positive slope magnitude into percent, ratio, and degrees. Enter vertical change and horizontal plan distance in the same unit. The calculator does not preserve uphill or downhill direction. For a fall, enter the positive amount of fall and record direction separately from field notes or survey data. It rejects zero and negative inputs. The result is a geometry check, not a survey, drainage design, accessibility determination, vehicle-clearance study, or code approval.
Quick answer
Percent grade equals rise divided by run, multiplied by 100.
What this tells you
- •Percent grade equals rise divided by run, multiplied by 100.
- •A 1:20 slope is the same steepness as a 5.0% grade and a 2.9 degree angle.
- •Use horizontal run, not the sloped pavement or ground distance.
- •Keep rise and run in the same unit before you calculate.
- •Both inputs must be finite and greater than zero, so flat, negative, and signed-direction entries return no result.
- •Percent grade and angle display to 1 decimal place, while the run-per-rise ratio rounds to no more than 2 decimals.
- •The formula reports steepness magnitude only. Record uphill, downhill, drainage, or station direction elsewhere.
How to Use
- 1Measure the vertical change over the stretch you want to check.
- 2Measure the horizontal run over the same stretch.
- 3Enter both numbers in the same unit, such as feet and feet or inches and inches. If the slope falls instead of rises, enter the fall as a positive change amount.
- 4Calculate to see the percent grade, slope ratio, and angle.
- 5Use the result as a geometry check, then compare it with surveyed elevations, project drawings, manufacturer limits, and local requirements.
- 6Confirm that run is horizontal plan distance. Do not substitute the longer distance measured along the sloped surface.
- 7For real construction or access design, have a qualified professional review transitions, cross slope, drainage, traction, and code details.
How It Works
Formula
Percent Grade = (Rise / Run) x 100
Slope Ratio = 1 : (Run / Rise)
Angle = atan(Rise / Run) x 180 / piAll outputs come from positive rise divided by positive horizontal run. Multiplying that quotient by 100 gives percent grade. Dividing run by rise gives X in the displayed 1:X ratio. Arctangent of rise divided by run, converted from radians to degrees, gives angle. Percent and angle round to 1 decimal place. Run per rise rounds to 2 decimals and unnecessary trailing zeros are removed from the ratio string. For rise 1.5 and run 18.75, grade is 8.0%, ratio is 1:12.5, and angle is 4.6 degrees. Negative signs are not interpreted as direction because the validation rejects them.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
2 feet of rise over 40 feet of run
Divide 2 by 40 to get 0.05, then multiply by 100 for a 5.0% grade. The same slope reads as 1:20 because 40 divided by 2 is 20.
1 foot of rise over 12 feet of run
This is a common reference slope. The percent grade is 1/12 x 100 = 8.3%, and the angle is about 4.8 degrees.
3 feet of rise over 24 feet of run
Shorter run for the same rise makes the grade steeper. Here the site climbs 1 unit for every 8 units of horizontal travel.
Decimal rise and run
Dividing 1.5 by 18.75 gives 0.08. The ratio uses 18.75 divided by 1.5, which is 12.5, and arctangent of 0.08 rounds to 4.6 degrees.
Same grade in inches
Using inches for both inputs gives the same quotient as 2 feet over 40 feet. Matching units cancel in the ratio.
Downhill magnitude
The calculator returns the same positive magnitude for a 2-foot fall. It does not label direction, so note downhill orientation separately and do not enter -2.
Common Grade Reference Points
Quick slope conversions for site and driveway planning.
| Slope Ratio | Percent Grade | Angle | Typical read |
|---|---|---|---|
| 1:40 | 2.5% | 1.4° | Light yard fall |
| 1:20 | 5.0% | 2.9° | Moderate site grade |
| 1:12 | 8.3% | 4.8° | Noticeably steep |
| 1:10 | 10.0% | 5.7° | Steep driveway |
| 1:8 | 12.5% | 7.1° | Very steep approach |
These reference points describe geometry only. They do not replace project drawings, drainage design, or local code review.
How to read an elevation grade
Percent grade tells you how much vertical change happens over 100 matching units of horizontal run. A 5% grade means 5 units of rise for every 100 units of run, or 1 unit of rise for every 20 units of run.
Slope ratio is often easier to picture in the field because it reads as 1:X. Angle is useful when you are checking equipment specs, ramps, or cut and fill sketches that call out degrees.
For driveways and site work, this is a first-pass geometry check. Surface traction, drainage paths, transitions at the street or garage, and local requirements can change what is practical to build.
Rise must come from elevations tied to one consistent datum or benchmark. Mixing assumed grade, local benchmark, and survey-datum elevations can create a false vertical change. Instrument accuracy, rod readings, station locations, and earthwork tolerances also affect field results.
Longitudinal grade is not cross slope. A driveway, ramp, road, or drainage surface can have both, plus vertical curves and transition zones. One rise and run cannot describe those changes or confirm compliance at every point.
Common mistakes
- Mixing units, such as entering rise in inches and run in feet
- Using the sloped driveway or ground distance instead of horizontal run
- Reading 5% grade as 1:5 instead of 1:20
- Assuming the geometry result alone settles drainage, traction, or permit questions
- Entering a negative fall even though this calculator accepts positive magnitude only
- Mixing elevations from different survey datums, benchmarks, or measurement stations
- Checking one average grade while missing steeper local segments, cross slopes, and transitions
- Using rounded output as a construction control value without the required survey precision and tolerances
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