CADGISHow to use the calculator
- Choose Elevations → Slope if you know two elevations and the horizontal distance between them. Choose Slope → Elevation if you know a starting elevation and a grade or angle.
- Pick the units for distance and elevation. If they differ, the calculator converts them for you (1 ft = 0.3048 m).
- Enter the values and press Calculate or Enter. After that, results update as you type.
- Adjust the decimal places, then press Copy results.
Grade, slope ratio, slope angle and elevation difference
These four values describe the same slope in different ways:
- Elevation difference (ΔZ) is how much higher or lower Point B is than Point A. Positive means uphill, negative means downhill.
- Grade (%) is the rise per 100 units of horizontal distance. A 5% grade rises 5 m over 100 m. It's common for roads, pipes and drainage.
- Slope ratio gives the horizontal distance for each unit of rise, shown here as
1 : H(vertical : horizontal). A 5% grade is 1 : 20. - Slope angle is the angle between the slope and the horizontal, in degrees. A 5% grade is about 2.8624°.
Formulas
Elevations → slope
ΔZ = ZB − ZA
Grade (%) = ΔZ ÷ Horizontal distance × 100
Slope ratio = 1 : (Horizontal distance ÷ |ΔZ|)
Slope angle = atan(|ΔZ| ÷ Horizontal distance)
Slope → elevation
From grade: ΔZ = Horizontal distance × Grade ÷ 100
From angle: ΔZ = Horizontal distance × tan(angle)
Ending elevation = Starting elevation ± ΔZ
Use horizontal distance, not the distance measured along the slope. When distance and elevation are in different units, both are converted to meters before calculating.
Worked examples
Example 1: slope between two levels
Point A is at 100.000 m and Point B at 105.000 m, 100.000 m apart horizontally. ΔZ = +5.000 m, grade = 5 ÷ 100 × 100 = 5.00 %, ratio = 1 : 20.00, and angle = atan(0.05) = 2.8624°, uphill.
Example 2: a road falling at 6%
Starting elevation 250.000 m, horizontal distance 80.000 m, grade 6% downhill. ΔZ = 80 × 6 ÷ 100 = −4.800 m, so the ending elevation is 245.200 m. The ratio is 1 : 16.67 and the angle is 3.4336°.
Example 3: angle in feet
Horizontal distance 150.000 ft at a 2° slope uphill. ΔZ = 150 × tan 2° = +5.238 ft, which is a grade of 3.49 % and a ratio of 1 : 28.64.
Common slopes
| Grade | Slope ratio (V : H) | Slope angle |
|---|---|---|
| 1% | 1 : 100 | 0.5729° |
| 2% | 1 : 50 | 1.1458° |
| 5% | 1 : 20 | 2.8624° |
| 8.33% | 1 : 12 | 4.7636° |
| 10% | 1 : 10 | 5.7106° |
| 33.33% | 1 : 3 | 18.4349° |
| 50% | 1 : 2 | 26.5651° |
| 100% | 1 : 1 | 45.0000° |
Frequently asked questions
Is a 100% grade vertical?
No. A 100% grade rises one unit for every unit of horizontal distance, which is 45°. A vertical face would have an infinite grade.
Why do some drawings show ratios like 3:1?
Earthworks drawings often write slopes as horizontal : vertical, so 3:1 (H:V) means 3 m across for every 1 m up. That's the same slope as 1 : 3 in this calculator's vertical : horizontal format. Always check which convention a drawing uses.
Can I use negative elevations?
Yes. Elevations below a datum, such as −2.500 m, work normally. Only the horizontal distance must be greater than zero.
Can I mix feet and meters?
Yes. Choose the unit for distance and for elevation separately. The calculator converts internally using the international foot (0.3048 m), and shows elevations in your chosen elevation unit.