Important Note : Slope, angle, and percent grade all describe the same line. Percent grade is rise ÷ run × 100, while a vertical line has undefined slope because its run is 0.

Use this Slope Calculator to find the slope of a line, angle, percent grade, line equation, y-intercept, rise/run, and distance using the method you need. It is useful for algebra, graphing, geometry, surveying, construction, and any situation where you need to describe how steep a line is.

Reviewed by: AjaxCalculators Editorial Team
Last updated: April 24, 2026
Method source: Standard slope-of-a-line formulas using rise over run, angle conversion, percent grade conversion, and distance between two points
Editorial standards: AjaxCalculators Editorial Policy

What This Slope Calculator Calculates

This calculator supports four common slope methods:

• Two points
• Point + slope
• Point + angle
• Point + percent grade

Depending on the method, it can show:

• Slope (m)
• Angle
• Percent grade
• Vertical line status
• Line equation
• y-intercept
• Distance between points
• Rise / Run

How the Slope Calculator Works

1) Slope from Two Points

If you know two points on the line, the slope formula is:

m = (y₂ − y₁) / (x₂ − x₁)

This is the standard rise-over-run formula.

The rise is the vertical change and the run is the horizontal change.

2) Angle from Slope

The line angle comes from the inverse tangent of the slope:

θ = arctan(m)

This lets the calculator convert ordinary slope into degrees, radians, or grads.

3) Percent Grade

Percent grade is another way to express the same slope:

Percent grade = 100 × m

This matches the standard “rise divided by run, then multiplied by 100” rule used for slope in percent form.

4) Distance Between Two Points

If two points are known, the calculator also finds the straight-line distance:

d = √[(x₂ − x₁)² + (y₂ − y₁)²]

This is the standard distance formula in coordinate geometry.

Why Slope, Angle, and Percent Grade Are Connected

These are not separate ideas. They all describe the same line in different formats.

• Slope is rise divided by run
• Angle is the geometric direction of that slope
• Percent grade is slope multiplied by 100

That is why the calculator can move between them depending on the method you choose.

Special Cases

• Horizontal line: slope is 0
• Vertical line: slope is undefined because the run is 0

This is why the live page includes a separate Vertical line? result.

Worked Example

Suppose the line passes through the points (2, 3) and (8, 15).

Step 1: Find the rise
Rise = 15 − 3 = 12

Step 2: Find the run
Run = 8 − 2 = 6

Step 3: Find the slope
m = 12 / 6 = 2

Step 4: Find percent grade
Percent grade = 100 × 2 = 200%

Step 5: Find the angle
θ = arctan(2) ≈ 63.43°

Step 6: Find the distance
d = √[(8 − 2)² + (15 − 3)²] = √(36 + 144) = √180 ≈ 13.42

How to Use This Slope Calculator

1. Choose the calculation method you want.
2. Enter the required values for that method.
3. Select the angle unit if needed.
4. Click Calculate.
5. Review the slope, angle, percent grade, equation, intercept, and any extra outputs shown.

How to Interpret the Result

Slope (m) tells you how much the line rises or falls for each unit of horizontal run.

Angle tells you the steepness in angular form.

Percent grade tells you the same steepness in percentage form.

Line equation gives the algebraic description of the line.

y-intercept tells you where the line crosses the y-axis.

Distance between points gives the straight-line separation when two points are used.

Practical Uses of a Slope Calculator

• find the slope of a line from two points
• convert slope into angle or percent grade
• write the equation of a line
• check graphing and algebra homework
• estimate steepness in geometry, surveying, or construction work

References

1. OpenStax Intermediate Algebra 2e – slope formula between two points
2. OpenStax Elementary Algebra 2e – slope as rise over run, horizontal and vertical line cases
3. OpenStax Prealgebra 2e – undefined slope for vertical lines
4. USGS – percent slope and angle from rise and run
5. AjaxCalculators live Slope Calculator

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Disclaimer: This calculator is for educational and practical math use. Slope, angle, and percent grade are just different ways to describe the same rise-over-run relationship, while vertical lines are a special case with undefined slope.