# Slope Calculator

> Slope m = (y₂ − y₁) ÷ (x₂ − x₁), so the line through (2, 3) and (8, 7) has a slope of 4/6 = 2/3 (about 0.667), an angle of 33.69° and the equation y = (2/3)x + 5/3. You can also enter a rise and run for ramps and roofs, or find a point a set distance along a slope.

- Interactive calculator: https://calculatorswithsteps.com/slope-calculator
- Category: Math & Statistics Calculators
- Last updated: 2026-11-10
- Publisher: Calculators With Steps (calculatorswithsteps.com)

## How to use the slope calculator

Choose what you know:

- **Two points:** enter (x₁, y₁) and (x₂, y₂). Coordinates can be negative, decimals or fractions such as 1/2.
- **Rise and run:** enter the vertical rise and horizontal run, for example a ramp, roof, driveway or hill.
- **A point, slope and distance:** enter a starting point, the slope and how far to travel along the line to get the two points at that distance.

The two-point result shows the slope as a reduced fraction and a decimal, the rise and run, the angle, the percent grade, the distance and midpoint, both intercepts and the equation of the line in three forms.

## The slope formula

**m = (y₂ − y₁) ÷ (x₂ − x₁) = rise ÷ run**

- **m** is the slope (gradient).
- **y₂ − y₁** is the rise, the change in height.
- **x₂ − x₁** is the run, the horizontal change.

It does not matter which point you call the first, as long as you subtract in the same order on the top and the bottom.

## Worked example: (2, 3) and (8, 7)

| Quantity | Working | Result |
| --- | --- | --- |
| Rise | 7 − 3 | 4 |
| Run | 8 − 2 | 6 |
| Slope | 4 ÷ 6 | 2/3 ≈ 0.666667 |
| y-intercept | 3 − (2/3) × 2 | 5/3 |
| Angle | arctan(2/3) | 33.69° |
| Grade | 2/3 × 100 | 66.67% |
| Distance | √(6² + 4²) = √52 | 2√13 ≈ 7.211103 |
| Midpoint | ((2 + 8) ÷ 2, (3 + 7) ÷ 2) | (5, 5) |

The equation of the line in each form:

- **Slope-intercept:** y = (2/3)x + 5/3
- **Point-slope:** y − 3 = (2/3)(x − 2)
- **Standard:** 2x − 3y = −5

The distance uses the Pythagorean theorem on the rise and run; the [Pythagorean theorem calculator](https://calculatorswithsteps.com/pythagorean-theorem-calculator) explains that step in more detail.

## Positive, negative, zero and undefined slopes

| Slope | Line | Example points | Result |
| --- | --- | --- | --- |
| Positive | Rises left to right | (2, 3), (8, 7) | 2/3 |
| Negative | Falls left to right | (−2, 1), (4, −3) | −2/3 |
| Zero | Horizontal | (0, 4), (5, 4) | 0, y = 4 |
| Undefined | Vertical | (3, 2), (3, 9) | x = 3 |

## Slope as grade, angle and pitch

Builders, road engineers and roofers describe the same slope in different ways. Grade is the slope as a percentage (rise ÷ run × 100), the angle comes from the inverse tangent, and roof pitch is the rise for every 12 units of run.

| Rise : run | Slope | Grade | Angle |
| --- | --- | --- | --- |
| 1 : 12 | 0.083333 | 8.33% | 4.76° |
| 1 : 4 | 0.25 | 25% | 14.04° |
| 4 : 12 roof | 0.333333 | 33.33% | 18.43° |
| 6 : 12 roof | 0.5 | 50% | 26.57° |
| 1 : 1 | 1 | 100% | 45° |
| 2 : 1 | 2 | 200% | 63.43° |

A 100% grade is a 45° angle, not a vertical wall, which surprises a lot of people. Because grade is a ratio, the [percentage calculator](https://calculatorswithsteps.com/percentage-calculator) and the [ratio calculator](https://calculatorswithsteps.com/ratio-calculator) are useful for related conversions.

**Ramps.** The ADA Standards for Accessible Design limit the running slope of a wheelchair ramp to 1:12. For a 30-inch rise, enter rise 30 and run 360 to confirm 8.33%.

## Tips

- Keep rise and run in the same unit. Mixing inches and feet makes the slope 12 times too big or too small.
- The angle of inclination is measured counter-clockwise from the positive x-axis, so it runs from 0° up to (but not including) 180°. A negative slope gives an angle above 90°.
- Parallel lines have equal slopes. Perpendicular lines have slopes that multiply to −1, such as 2/3 and −3/2.
- To find the point a given distance along a line, use the third mode. From (2, 3) along a slope of 3/4, the points 10 units away are (10, 9) and (−6, −3).

## Frequently asked questions

### How do you find the slope with two points?

Subtract the y-values, subtract the x-values in the same order, and divide: m = (y₂ − y₁) ÷ (x₂ − x₁). For (2, 3) and (8, 7), m = (7 − 3) ÷ (8 − 2) = 4 ÷ 6 = 2/3, about 0.666667.

### What is the slope formula?

Slope is rise over run: m = (y₂ − y₁) ÷ (x₂ − x₁). The rise is the vertical change and the run is the horizontal change between two points on the line.

### How do you convert a slope to a percentage?

Multiply the slope by 100. A ramp that rises 1 unit for every 12 units of run has a slope of 1/12, which is an 8.33% grade.

### How do I convert a slope to degrees?

Take the inverse tangent of the slope: angle = arctan(rise ÷ run). A roof that rises 6 inches per 12 inches of run has a slope of 0.5, which is 26.57°.

### What is the slope of a vertical or horizontal line?

A horizontal line has a slope of 0 because the rise is 0. A vertical line has an undefined slope because the run is 0 and you cannot divide by zero. The line through (3, 2) and (3, 9) is vertical, with equation x = 3.

### How do I write the equation of a line from two points?

Find the slope, then the y-intercept b = y₁ − m × x₁, and write y = mx + b. For (2, 3) and (8, 7), m = 2/3 and b = 3 − (2/3) × 2 = 5/3, so y = (2/3)x + 5/3, or 2x − 3y = −5 in standard form.

### What is the maximum slope for a wheelchair ramp?

The 2010 ADA Standards allow a running slope of no more than 1:12, an 8.33% grade or about 4.76°. A ramp that climbs 30 inches therefore needs at least 360 inches (30 feet) of run.

### What does a negative slope mean?

The line falls as you move from left to right. The line through (−2, 1) and (4, −3) has a slope of −4 ÷ 6 = −2/3, and its angle of inclination is 146.31° measured from the positive x-axis.

## Sources

- [Wikipedia – Slope](https://en.wikipedia.org/wiki/Slope)
- [Wolfram MathWorld – Slope](https://mathworld.wolfram.com/Slope.html)
- [U.S. Access Board – ADA Accessibility Standards (ramps, section 405)](https://www.access-board.gov/ada/)