CalculatorSlope
Calculate the slope of a line or surface from rise and run values using this straightforward geometry tool. Slope measures steepness and direction of change — a concept that appears in coordinate geometry, physics (inclined planes), construction (roof pitch and ramps), road engineering (grade percentage), and data analysis (rate of change in graphs). Enter the rise and run values and get the slope instantly, expressed as a decimal and as a ratio.
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Slope Calculator
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Slope is commonly calculated as rise divided by run.
How To Use Slope Calculator
- Enter the rise value — the vertical change (how much the line goes up or down).
- Enter the run value — the horizontal change (how far the line extends left or right).
- The tool divides rise by run to compute the slope: m = rise ÷ run.
- Review the slope result, which may be positive (upward slope), negative (downward slope), zero (flat), or undefined (vertical).
- Apply the slope value to your line equation, geometry problem, engineering specification, or data analysis.
Frequently Asked Questions
How is slope calculated?
Slope is calculated as rise divided by run: m = rise ÷ run. Rise is the vertical change between two points (y₂ − y₁) and run is the horizontal change (x₂ − x₁). For example, if a line rises 6 units over a horizontal distance of 4 units, the slope is 6 ÷ 4 = 1.5. A slope of 1.5 means the line rises 1.5 units for every 1 unit of horizontal distance.
What does a positive or negative slope mean?
A positive slope means the line rises from left to right — as x increases, y also increases. A negative slope means the line falls from left to right — as x increases, y decreases. A slope of zero means the line is perfectly horizontal. An undefined slope occurs when the run is zero (a vertical line), because division by zero is mathematically undefined.
How is slope used in construction and engineering?
In construction, slope is expressed as grade, pitch, or rise-to-run ratio. Roof pitch is expressed as rise over a 12-unit run (e.g., 4:12 means the roof rises 4 inches for every 12 inches of horizontal span). Wheelchair ramps are required to have a maximum slope of 1:12 (about 4.8°) for accessibility compliance. Road grades are expressed as percentages — a 5% grade rises 5 feet for every 100 feet of horizontal distance.
What is the slope-intercept form of a line?
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept (the value of y when x = 0). Once you have the slope from this calculator, you can substitute it into this equation along with any known point to write the full equation of the line. This is one of the most common tasks in algebra and analytic geometry.
Can this calculate slope from two coordinate points?
If you have two coordinate points (x₁, y₁) and (x₂, y₂), calculate the rise as y₂ − y₁ and the run as x₂ − x₁, then enter those values into this tool. The result will be the slope of the line connecting the two points. For example, for points (2, 3) and (6, 11): rise = 11 − 3 = 8, run = 6 − 2 = 4, slope = 8 ÷ 4 = 2.
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