Slope Calculator Guide: Rise Over Run & y = mx + b
Calculate slope with m = (y₂ − y₁) ÷ (x₂ − x₁). Full guide with rise over run, slope-intercept form y = mx + b, and grade percentage applications.
Slope Calculator — Direct Answer
Slope measures steepness: m = (y₂ − y₁) ÷ (x₂ − x₁), also known as rise over run. Between points (2, 3) and (6, 11): m = (11 − 3) ÷ (6 − 2) = 2. Slope is used in slope-intercept form y = mx + b, where m is slope and b is the y-intercept.
→ Calculate slope with our free slope calculator
How to Calculate Slope
Slope compares vertical change (rise) to horizontal change (run).
m = (y₂ − y₁) ÷ (x₂ − x₁)
Where:
- (x₁, y₁) = first point
- (x₂, y₂) = second point
- m = slope
How to identify rise and run
Rise = vertical change = y₂ − y₁ Run = horizontal change = x₂ − x₁
Example: From (0, 0) to (5, 10):
- Rise = 10
- Run = 5
- Slope = 10 ÷ 5 = 2
How to interpret slope types
| Slope | Type | Direction |
|---|---|---|
| Positive | Rising | Up and to the right |
| Negative | Falling | Down and to the right |
| Zero | Horizontal | Flat line |
| Undefined | Vertical | Straight up |
How to apply slope to slope-intercept form
Once you have slope, plug into y = mx + b:
Example: slope 2, point (3, 7)
- 7 = 2(3) + b
- 7 = 6 + b
- b = 1
- Equation: y = 2x + 1
Slope Chart by Grade Percentage
Slope as degrees, percent, and ratio
| Rise:Run | Degrees | Percent Grade | Note |
|---|---|---|---|
| 1:12 | 4.76° | 8.3% | ADA ramp max |
| 1:8 | 7.13° | 12.5% | Steep ramp |
| 1:4 | 14.04° | 25% | Standard roof pitch |
| 1:2 | 26.57° | 50% | Steep roof |
| 1:1 | 45.00° | 100% | 12:12 roof |
| 2:1 | 63.43° | 200% | Near vertical |
Slope of common surfaces
| Surface | Slope |
|---|---|
| ADA wheelchair ramp | 1:12 (8.3%) |
| Standard driveway | 2–5% |
| Concrete patio | 1–2% |
| Roof (low slope) | 2:12 |
| Roof (standard) | 4:12–8:12 |
| Roof (steep) | 12:12+ |
Common Slope Mistakes
Mistake 1: Reversing the formula
Writing (x₂ − x₁)/(y₂ − y₁) gives the reciprocal, not the slope. Fix: Rise (y) is always on top. Run (x) on bottom.
Mistake 2: Confusing slope with angle
Slope 1 (rise=run) is 45°, not 90°. 100% grade is not a vertical wall. Fix: Convert with angle = arctan(slope) and grade % = slope × 100.
Mistake 3: Dividing by zero
Vertical lines have undefined slope (not zero). Fix: If x₁ = x₂, slope is undefined. If y₁ = y₂, slope is zero.
Slope vs Other Linear Forms
Slope-intercept form
- Format: y = mx + b
- Best for: Graphing
- Shows: Slope + y-intercept
Point-slope form
- Format: y − y₁ = m(x − x₁)
- Best for: When you know slope and one point
- Shows: Slope + a point
Standard form
- Format: Ax + By = C
- Best for: Linear systems
- Shows: Coefficients
Slope Calculator FAQ
How do you calculate slope?
m = (y₂ − y₁) ÷ (x₂ − x₁). Subtract the y-values, subtract the x-values, divide.
What is rise over run?
Rise = vertical change. Run = horizontal change. Slope = rise ÷ run.
What is the slope of a horizontal line?
Zero. Horizontal lines have no rise (y doesn't change).
What is the slope of a vertical line?
Undefined. Vertical lines have no run (x doesn't change) → division by zero.
How do you convert slope to degrees?
Angle = arctan(slope). Slope 1 = 45°. Slope 0.5 = 26.57°.
Next Steps for Slope Math
- Slope Intercept Calculator — Slope and equation
- Distance Formula Calculator — Between points
- Math Calculator — All math tools
- Distance Formula Guide — Coordinate math
- Pythagorean Theorem Guide — Triangle math
Last updated October 2026. Slope is unitless when both axes use the same unit.