Slope Calculator

Name: Slope Calculator
Author: Jitendra Kumar

Find slope from two points with rise, run, decimal and fraction slope, percent grade, angle, intercepts, a coordinate preview, and step-by-step work.

Last Updated: April 24, 2026

Displayed precision

Controls rounded display only; the calculation uses full decimal input values.

Coordinate preview

Green shows rise. Amber shows run. The solid line connects the two points.

Slope

Rise / run

8 / 4

Fraction form

Line equation

y = 2x

Percent grade

200%

Angle

63.4349 deg

Step-by-step solution

Identify the two points
(1, 2) and (5, 10)
Keep the x and y coordinates paired so the substitutions stay consistent.
Find rise and run
rise = 10 - 2 = 8; run = 5 - 1 = 4
Rise is the vertical change. Run is the horizontal change.
Divide rise by run
m = 8 / 4 = 2
Slope is the ratio of vertical change to horizontal change.
Build the line equation
y = 2x
Use y = mx + b with one point to solve for the y-intercept.

The line rises 8 unit(s) for every 4 unit(s) of horizontal run.

Slope type

positive

Y-intercept

X-intercept

Math Learning Notice

This calculator is intended for algebra practice, homework checks, and planning calculations. Follow your class, project, or engineering standard when specific notation or precision rules are required.

Reviewed For Methodology, Labels, And Sources

Every CalculatorWallah calculator is published with visible update labeling, linked source references, and founder-led review of formula clarity on trust-sensitive topics. Use results as planning support, then verify institution-, policy-, or jurisdiction-specific rules where they apply.

Reviewed By

Jitendra Kumar, Founder & Editorial Standards Lead, oversees methodology standards and trust-sensitive publishing decisions.

Review editor profile

Topic Ownership

Sales tax and tax-sensitive estimate tools, Education and GPA planning calculators, Health, protein, and screening-formula pages, Platform-wide publishing standards and methodology

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Methodology & Updates

Page updated April 24, 2026. Trust-critical pages are reviewed when official rates or rules change. Evergreen calculator guides are checked on a recurring quarterly or annual cycle depending on topic volatility.

Sources & methodology About the review process

How to Use This Calculator

Step 1: Enter the first point
Type the x1 and y1 coordinates exactly as they appear in the ordered pair.
Step 2: Enter the second point
Type x2 and y2 for the second ordered pair, keeping each x-value with its matching y-value.
Step 3: Review rise and run
The calculator subtracts y-values for rise and x-values for run before dividing.
Step 4: Check the slope result
Read slope as a decimal, fraction form when available, percent grade, and angle.
Step 5: Use the equation output
Use y = mx + b for non-vertical lines, or x = constant for a vertical line.

How This Calculator Works

The calculator starts with two ordered pairs, labels them as (x1, y1) and (x2, y2), then computes the vertical change and horizontal change. The vertical change is rise: y2 - y1. The horizontal change is run: x2 - x1.

For any non-vertical line, slope is rise divided by run. The result is shown as a rounded decimal and, when rise and run are whole numbers, as a reduced fraction. The same slope is also converted to percent grade by multiplying by 100 and to an angle by using arctangent.

If the run is zero, the line is vertical and the slope is undefined. If the rise is zero, the line is horizontal and the slope is 0. These cases are separated because they are common sources of classroom mistakes.

What You Need to Know

What Is Slope?

Slope measures how much a line changes vertically compared with how much it changes horizontally. In algebra, it is often described as rise over run. In practical settings, the same idea appears as grade, incline, rate of change, or steepness.

The sign of the slope tells you direction. A positive slope rises as x increases. A negative slope falls as x increases. A zero slope is flat. A vertical line has no numeric slope because the horizontal change is zero.

Type	Condition	Meaning
Positive slope	m > 0	The line rises from left to right.
Negative slope	m < 0	The line falls from left to right.
Zero slope	m = 0	The line is horizontal because rise is zero.
Undefined slope	run = 0	The line is vertical because division by zero is not defined.

Slope Formulas

Formula	Expression	Use
Slope formula	m = (y2 - y1) / (x2 - x1)	Find slope from two coordinate points.
Rise	y2 - y1	Vertical change between the points.
Run	x2 - x1	Horizontal change between the points.
Percent grade	slope x 100	Useful for ramps, roads, roofs, and incline descriptions.
Slope-intercept form	y = mx + b	Use slope and y-intercept to describe a non-vertical line.

Coordinate Geometry Connections

Slope connects naturally with the Pythagorean theorem calculator because rise and run form the legs of a right triangle. Use slope for steepness and the Pythagorean theorem for distance.

It also connects with the math equation solver when slope appears inside a larger algebra problem, and with the angle converter when a slope angle needs to move between degrees and radians.

Keep the research moving with Math Equation Solver, Scientific Calculator, Pythagorean Theorem Calculator, and Angle Converter.

Frequently Asked Questions

A slope calculator finds the steepness and direction of a line from two coordinate points. It computes rise, run, slope as a decimal, fraction form when possible, percent grade, angle, and the line equation.

The slope formula is m = (y2 - y1) / (x2 - x1). The numerator is vertical change, called rise, and the denominator is horizontal change, called run.

An undefined slope means the run is zero because both points have the same x-value. The line is vertical, so the formula would require division by zero.

A zero slope means the rise is zero because both points have the same y-value. The line is horizontal and can be written as y = constant.

A positive slope rises from left to right, while a negative slope falls from left to right. In the formula, the sign comes from the ratio of rise to run.

Yes. For non-vertical lines, it returns slope-intercept form y = mx + b and point-slope form. For vertical lines, it returns the equation x = constant.

Percent grade is slope multiplied by 100. For example, a slope of 0.08 is an 8% grade. It is commonly used for roads, ramps, roofs, and incline descriptions.

No, as long as each x and y value stays with its original point. Reversing both points changes the signs of rise and run together, so the slope stays the same.

Yes. The calculator supports whole numbers, decimals, and negative coordinates for all four point inputs.

For a straight line, yes. Slope describes the constant rate of change in y for each one-unit change in x.