Slope Calculator
What Is a Slope Calculator?
A slope calculator finds the steepness of a line or surface expressed as slope (rise/run), angle in degrees, or percent grade. These three representations all describe the same thing — how much a surface rises or falls per unit of horizontal distance — but different fields use different conventions: math uses slope, civil engineering uses percent grade, and roof framing uses pitch (rise per 12 inches of run).
Slope formula from two points: m = (y2 − y1) / (x2 − x1). A slope of 0.25 means the surface rises 0.25 units for every 1 unit of horizontal travel. That equals a 25% grade or a 14.04° angle.
This calculator works from any starting representation — two coordinate points, rise and run measurements, a known angle, or a known percent grade — and converts all three outputs simultaneously.
How to Use This Slope Calculator
- Choose your input method: two points, rise & run, angle in degrees, or percent grade.
- Enter the known values for your chosen method.
- Click Calculate Slope to see slope, angle, and percent grade simultaneously.
- Use the direction label to confirm positive (uphill) or negative (downhill) slope.
Slope Conversion Reference Table
| Slope (m) | Percent Grade | Angle | Common Use |
|---|---|---|---|
| 0.01 | 1% | 0.57° | ADA ramp minimum drainage |
| 0.083 | 8.33% | 4.76° | ADA maximum ramp slope |
| 0.15 | 15% | 8.53° | Steep driveway |
| 0.25 | 25% | 14.04° | Steep hill, challenging grade |
| 0.333 | 33.3% | 18.43° | Steep ski slope (blue run) |
| 0.5 | 50% | 26.57° | Low-pitch roof (6:12) |
| 1.0 | 100% | 45° | 45-degree angle, steep roof |
Slope Formulas Reference
- From two points: m = (y2 − y1) / (x2 − x1)
- From rise and run: m = rise / run
- Percent grade to slope: m = grade% / 100
- Angle to slope: m = tan(angle in degrees)
- Slope to angle: angle = arctan(m) × (180/π)
- Slope to percent grade: grade% = m × 100
Real-World Slope Applications
- Driveways: Maximum comfortable grade is 15–20%. Above 20% causes cars to bottom out and becomes hazardous in snow/ice.
- ADA ramps: Maximum slope is 1:12 (8.33%) per ADA standards. Cross-slope must be under 2%.
- Roof pitch: Expressed as rise per 12 inches of run. A 6:12 pitch has slope 0.5 = 50% grade = 26.57°.
- Road grades: Interstate highways are typically limited to 6% grade. Steep mountain roads reach 12–14%.
- Drainage: Minimum 1% slope away from building foundations to prevent water pooling.
- Algebra: Slope is the 'm' in y = mx + b (slope-intercept form), describing how steep a line is on a coordinate plane.
Frequently Asked Questions About Slope
How do I calculate slope from two points?
Subtract the y-coordinates (rise) and divide by the difference in x-coordinates (run). For points (2, 3) and (6, 11): slope = (11−3)/(6−2) = 8/4 = 2.
What is a 5% slope in degrees?
5% grade = slope of 0.05. Angle = arctan(0.05) = 2.86°. A gentle, barely noticeable incline.
What does a negative slope mean?
A negative slope means the line or surface goes downhill as you move from left to right (x increases, y decreases). On a graph, it slopes from upper-left to lower-right.
What is the maximum slope for a driveway?
Most building codes allow 15–20% maximum for residential driveways. Above 20% risks hydroplaning in rain and loss of traction in ice/snow. Some jurisdictions limit to 12–14%.
How do I find slope from rise and run?
Divide rise by run. If a ramp rises 3 feet over 36 feet of horizontal distance: slope = 3/36 = 0.0833 = 8.33% grade.
What is a 45-degree slope in percent?
45° = 100% grade (rise equals run). tan(45°) = 1. This is quite steep — equivalent to a very aggressive ski slope or a very steep roof.
What is the slope of a horizontal line?
A perfectly flat (horizontal) line has a slope of 0 — no rise over any run. A vertical line has undefined slope (division by zero — infinite rise, zero run).
How is slope used in construction?
Roof pitch, ramp grades, drainage slopes, staircase rise-to-run ratios, and road grades all use slope calculations. OSHA, ADA, and local building codes specify maximum and minimum slopes for safety and accessibility.