Calculate rise, run, slope, and inclination angle from two points on a coordinate plane.
Complete the required fields and select the calculate button.
The two x-coordinates must differ. Equal x-values describe a vertical line whose slope is undefined.
This slope calculator finds the rate of change between two points on a coordinate plane. It compares the vertical change in y with the horizontal change in x, showing how much y rises or falls for each one-unit movement to the right.
Slope is used for straight-line equations, graphs, rates, calibration relationships, and trends. The two x-coordinates must differ. If they are equal, the line is vertical and its slope is undefined rather than an ordinary number.
Coordinates may be positive, negative, or decimal. Use compatible units on each axis and state them with the answer when the points represent measurements.
m = (y₂ − y₁) ÷ (x₂ − x₁)
The denominator cannot be zero. Reversing both differences gives (y₁ − y₂)/(x₁ − x₂), which is equivalent. Reversing only one difference changes the sign incorrectly.
| Symbol or result | Meaning |
|---|---|
| (x₁, y₁) | The first coordinate pair. |
| (x₂, y₂) | The second coordinate pair. |
| Δx | Horizontal change x₂ − x₁; it must be nonzero. |
| Δy | Vertical change y₂ − y₁. |
| m | Slope, or vertical units per horizontal unit, displayed to two decimals. |
For points (2, 3) and (8, 15), Δy = 15 − 3 = 12 and Δx = 8 − 2 = 6. The slope is 12 ÷ 6 = 2.00.
This means y increases by two units for every one-unit increase in x along the line. Checking in reverse gives (3 − 15)/(2 − 8) = −12/−6 = 2.
A positive slope rises from left to right; a negative slope falls. Zero describes a horizontal line. Larger absolute values indicate more vertical change per horizontal unit, but comparisons make sense only with compatible axis scales.
Slope between two observations is a secant rate of change. It does not prove the relationship is linear between or beyond them. For measured data, uncertainty and rounding affect the result, especially when x values are close. A fitted regression slope uses all selected observations and is a different calculation.
The line through two points can be written in point-slope form as y − y₁ = m(x − x₁). Once m is known, substituting either point gives an equation for the same line. In slope-intercept form y = mx + b, calculate b as y₁ − mx₁. Substituting the second point is a useful independent check.
When slope represents a rate, direction matters. A result of −3 dollars per item means the modeled y value falls by three dollars for each additional item; it is not merely a steepness of three. A reciprocal slope answers a different question and is valid only when the original numerator is nonzero.
Close x-coordinates make the denominator small, which magnifies coordinate error. Record enough significant digits and consider an uncertainty analysis for measured points. In a graph, axis scaling can make the same numeric slope appear visually steep or flat, so read the labels rather than judging from appearance.
Parallel nonvertical lines share the same slope. Perpendicular nonvertical lines have slopes whose product is −1, provided neither is horizontal or vertical; the perpendicular slope is the negative reciprocal. These rules offer useful checks in geometry but still require attention to exceptional lines. Plotting both points provides another quick check of direction and sign.
Keep the original inputs beside the result for a clear, reproducible record.
Equal x values make the horizontal change zero, so the formula divides by zero. That vertical line has undefined slope.
It means y decreases as x increases along the line. The units state how much decrease occurs per horizontal unit.
Yes. Equal y-coordinates produce zero vertical change and a horizontal line, provided the x values differ.
No, if both numerator and denominator orders are reversed. Both differences change sign, leaving their quotient unchanged.
The page formats the result to two places. Preserve the fraction or calculate separately when greater precision is required.
Only when both axes measure the same unit. Otherwise it has units such as metres per second or dollars per item.
No. Two-point slope uses exactly two coordinates; regression estimates a relationship from a collection of observations.