Free slope calculator finds slope from two points instantly. Get slope formula, y-intercept, angle, and line equation. Shows step-by-step solution with graph.
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Finding slope between two points is fundamental in algebra and has countless real-world applications from construction to data analysis. Our slope calculator uses the formula m = (y₂ - y₁) / (x₂ - x₁) to instantly calculate the slope, also known as gradient or rate of change. Simply enter two coordinate points and get the slope as a decimal, fraction, angle, and percentage grade—plus the complete line equation in multiple forms.
Slope measures the steepness and direction of a line. Also called gradient, grade, or incline, slope represents the ratio of vertical change (rise) to horizontal change (run) between any two points on a line. A positive slope rises from left to right, a negative slope falls, zero slope is horizontal, and undefined slope is vertical. Understanding slope is essential for linear equations, graphing, and real-world applications like calculating roof pitch, wheelchair ramp angles, and road grades.
Slope Formula
m = (y₂ - y₁) / (x₂ - x₁) = rise / runGet slope, angle, distance, and line equations instantly without manual math errors.
View slope as decimal, simplified fraction, angle in degrees, and percent grade for construction.
See exactly how the slope formula is applied with detailed mathematical steps.
Interactive coordinate plane shows your line with the rise/run triangle.
Get slope-intercept (y=mx+b), point-slope, and standard form equations instantly.
Complete algebra assignments with step-by-step solutions showing the slope formula in action.
Generate examples, verify student work, and demonstrate slope concepts with visual graphs.
Calculate roof pitch, drainage slopes, and ensure proper grades for concrete work.
Verify wheelchair ramp slopes meet ADA requirements (maximum 1:12 ratio or 8.33% grade).
Design road grades, calculate cut/fill slopes, and plan drainage systems.
Find trend line slopes in scatter plots and calculate rates of change in datasets.
The slope formula is m = (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are two points on the line. This calculates 'rise over run'—the vertical change divided by horizontal change. For example, for points (2, 3) and (4, 7): m = (7-3)/(4-2) = 4/2 = 2.
To find slope from two points: (1) Subtract the y-coordinates to get the rise: y₂ - y₁. (2) Subtract the x-coordinates to get the run: x₂ - x₁. (3) Divide rise by run: m = rise/run. The order of subtraction doesn't matter as long as you're consistent.
A slope of 0 means the line is horizontal (perfectly flat). The y-value stays constant regardless of x, so the equation is simply y = b where b is the y-intercept. Examples include a flat floor or level shelf.
Undefined slope occurs for vertical lines where x₁ = x₂. Since the run (denominator) is zero and division by zero is undefined, vertical lines have no numerical slope. The equation is x = a constant.
Use the arctangent (inverse tangent) function: angle = tan⁻¹(m). For example, a slope of 1 equals 45°, a slope of 2 equals about 63.43°, and a slope of 0.5 equals about 26.57°. Our calculator does this conversion automatically.
Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept (where the line crosses the y-axis). This is the most common form for linear equations because it immediately shows the slope and starting point.
Point-slope form is y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is any known point on the line. This form is useful when you know the slope and a point but not the y-intercept.
Parallel lines have the same slope (m₁ = m₂). Perpendicular lines have slopes that are negative reciprocals: if one line has slope m, the perpendicular has slope -1/m. For example, if m = 2, the perpendicular slope is -1/2.
Percent grade is slope expressed as a percentage: (rise/run) × 100. A 10% grade means 10 feet of rise for every 100 feet of run. Road signs showing '6% Grade' mean the road rises or falls 6 feet per 100 feet of horizontal distance.
The ADA (Americans with Disabilities Act) requires wheelchair ramps to have a maximum slope of 1:12 (1 inch of rise per 12 inches of run), which equals 8.33% grade or about 4.76°. Steeper ramps up to 1:8 (12.5%) are allowed for existing buildings when space is limited.