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Slope Calculator

Computes the slope of the line through two points (rise over run), its y- and x-intercepts, the slope-intercept equation y = mx + b, the angle of inclination and the distance between the points.

When to use

You have two points and need the gradient or the equation of the line through them.

Do not use when: You need a best-fit line through many points (use linear-regression) or only the distance between two points (use distance-2d).

Formula

m = (y₂ − y₁) / (x₂ − x₁); b = y₁ − m·x₁; x_intercept = −b / m; angle = atan(m) × 180/π; distance = √(Δx² + Δy²)

Inputs

Parameter	Type	Required	Description
`x1`	number	yes	x-coordinate of the first point.
`y1`	number	yes	y-coordinate of the first point.
`x2`	number	yes	x-coordinate of the second point.
`y2`	number	yes	y-coordinate of the second point.

Outputs

Output	Type	Unit	Description
`slope`	number		(y₂ − y₁) / (x₂ − x₁); omitted for a vertical line.
`slope_type`	string		'positive (rising)', 'negative (falling)', 'zero (horizontal line)' or 'undefined (vertical line)'.
`y_intercept`	number		Value of y where the line crosses the y-axis: y₁ − m·x₁.
`x_intercept`	number		Value of x where the line crosses the x-axis: −b / m (omitted for a horizontal line).
`equation`	string		Slope-intercept form y = mx + b (or x = c for a vertical line).
`angle_degrees`	number	°	atan(m) in degrees, between −90° and 90°.
`delta_x`	number		x₂ − x₁.
`delta_y`	number		y₂ − y₁.
`distance`	number		√(Δx² + Δy²).

Example

(1, 2) and (3, 6): {"x1":1,"y1":2,"x2":3,"y2":6} → {"slope":2,"slope_type":"positive (rising)","y_intercept":0,"x_intercept":0,"equation":"y = 2x","angle_degrees":63.4349,"delta_x":2,"delta_y":4,"distance":4.472136}

(0, 3) and (4, 1): {"x1":0,"y1":3,"x2":4,"y2":1} → {"slope":-0.5,"slope_type":"negative (falling)","y_intercept":3,"x_intercept":6,"equation":"y = -0.5x + 3","angle_degrees":-26.5651}

GET https://tttkmbb.com/api/v1/calculate/slope?x1=1&y1=2&x2=3&y2=6

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/slope (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/slope · Markdown: https://tttkmbb.com/math/slope.md · JSON definition: https://tttkmbb.com/math/slope.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="slope"
OpenAPI operationId: calculate_slope
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

FAQ

What happens for a vertical line?

Δx = 0, so the slope is undefined and no y-intercept exists. The calculator returns the equation x = constant, an angle of 90° and no slope value.

Is slope the same as gradient or grade?

Slope and gradient are the same ratio. A road grade is the slope expressed in percent (slope × 100).

Related calculators

Distance Between Two Points Calculator — Distance and midpoint of the same two points.
Linear Regression Calculator — Best-fit line through many points.
Angle Converter — Convert the inclination angle between degrees, radians and grades.