Math
Slope Calculator
Enter two points to find the slope, use a known slope to solve a missing coordinate, or start from an angle or a percentage grade. mathcheck gives you rise over run, equations, intercepts, the perpendicular slope, grade, angle, midpoint, distance, a graph, and plain-English interpretation.
The x-coordinate of the first point.
The y-coordinate of the first point.
The x-coordinate of the second point.
The y-coordinate of the second point.
Try an example
Result
Slope
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- Line equation
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- Angle
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- Grade
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- Perpendicular slope
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- Midpoint
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- Distance
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Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What is slope?
How steep a line is: how much y changes for each step right in x. measures how steep a line is. It compares vertical change (rise) to horizontal change (run) between any two points on the line.
What this calculator can solve
| Mode | Use it when | Output |
|---|---|---|
| Slope from two points | You know both ordered pairs | Slope, equations, intercepts, graph, midpoint, distance |
| Find missing y2 | You know P1, x2, and the slope | The missing y-coordinate plus the complete line |
| Find missing x2 | You know P1, y2, and a nonzero slope | The missing x-coordinate plus the complete line |
| Slope from an angle | You know the angle the line makes with the x-axis | m = tan θ, plus the line through P1 with that slope |
| Slope from a grade % | You know a road, ramp, or roof grade | m = grade / 100, plus the angle and the line through P1 |
How to find slope from two points
- Subtract the y-values to find the rise: y2 - y1.
- Subtract the x-values to find the run: x2 - x1.
- Divide rise by run and simplify the fraction.
- Use the slope and one point to write the equation of the line.
How to read the answer
- Positive slope means the line rises from left to right.
- Negative slope means the line falls from left to right.
- Zero slope means the line is horizontal.
- Undefined slope means the line is vertical, so the run is 0.
- The bigger the How far a number sits from zero, so the answer is never negative. of the slope, the steeper the line: a slope of 3 is steeper than a slope of 1/2.
Line equation forms
This calculator shows slope-A point where a graph crosses an axis. form and point-slope form because teachers commonly ask for both. Slope-intercept form is best when you want to see the y-intercept. Point-slope form is fastest when you already know one point and the slope.
Slope, angle, and grade are the same idea
A slope can be written three ways. As a ratio m (rise over run), as the angle of inclination θ the line makes with the x-axis, or as a percentage grade. The calculator always shows all three, and the angle and grade modes let you start from either one.
| Slope m | Angle θ | Grade |
|---|---|---|
| 0 | 0° | 0% |
| 1/12 ≈ 0.0833 | 4.76° | 8.33% (ADA ramp limit) |
| 1/2 | 26.57° | 50% |
| 1 | 45° | 100% |
| 2 | 63.43° | 200% |
| undefined | 90° | undefined |
Slope in the real world
Outside the classroom, slope is usually written as a grade, a pitch, or a ratio, but the math is identical: rise divided by run.
- Roads: highway signs give the grade as a percent. A 6% grade rises 6 feet for every 100 feet traveled horizontally (m = 0.06, about 3.4°). Long mountain grades are usually kept near 6% or below.
- Ramps: the ADA Standards limit the running slope of an accessible ramp to 1:12, which is 1 inch of rise per 12 inches of run, a slope of 1/12 ≈ 0.0833, or 8.33%. Steeper ramps need to be shorter and are only allowed in limited cases.
- Roofs: roof pitch is written as rise per 12 inches of run. A 6:12 roof has slope 6/12 = 1/2 (26.57°); a 12:12 roof has slope 1 (45°).
- Stairs: a typical stair rises about 7 inches per 11 inches of tread, a slope of 7/11 ≈ 0.64, or roughly 32°. Building codes cap riser height and set a minimum tread depth to keep that ratio comfortable.
- Trails and terrain: a 10% grade is a noticeable hill; 20% or more is steep enough that most people slow to a walk on a bike.
Parallel and perpendicular slopes
Parallel lines never meet, so they must rise at the same rate: they have the same slope. Perpendicular lines meet at a right angle, and their slopes are negative The number you get by flipping a fraction; 3/4 becomes 4/3, and 5 becomes 1/5. of each other. The Perpendicular slope tile shows -1/m for your line.
Perpendicular to slope 3/2
Flip 3/2 to 2/3 and change the sign: the perpendicular slope is -2/3. Check: (3/2) × (-2/3) = -1.
Common mistakes and edge cases
- Subtracting in different orders: use (y2 - y1) / (x2 - x1), not (y2 - y1) / (x1 - x2). Swapping both is fine; swapping one flips the sign.
- Reading undefined slope as 0. A vertical line has run 0, so the division is undefined; a horizontal line has rise 0, so the slope is 0.
- Typing 3/2 as 1.5 is fine, but typing 3/2 as 3.2 is not. Use decimals or the fraction's value in the slope field.
- Mixing angle units: 45 degrees is not 45 An angle unit where a full turn is 2π instead of 360 degrees.. The angle mode has a unit switch.
- Grade is not the angle. An 8.33% grade is only 4.76°, and a 100% grade is 45°, not 90°.
Worked examples
Positive slope
Line through (1, 2) and (5, 8)
Slope
3/2 (1.5)
Negative slope
Line through (-2, 7) and (4, -5)
Slope
-2
Find y2
P1 = (1, 2), x2 = 5, slope = 1.5
Slope
3/2 (1.5)
Find x2
P1 = (1, 2), y2 = 8, slope = 1.5
Slope
3/2 (1.5)
Horizontal line
Line through (-3, 4) and (6, 4)
Slope
0
Vertical line
Line through (2, -1) and (2, 5)
Slope
undefined
Slope from a 45° angle
θ = 45° gives m = tan 45° = 1
Slope
1
Slope from π/6 radians
θ = π/6 ≈ 0.5236 rad gives m = tan(π/6) = √3/3 ≈ 0.5774
Slope
0.5774
Vertical angle
θ = 90° is a vertical line, so the slope is undefined
Slope
undefined
ADA ramp grade
An 8.33% grade is the 1:12 ramp limit, slope ≈ 1/12 ≈ 0.0833
Slope
0.0833
12% road grade
A 12% grade is slope 12/100 = 3/25
Slope
3/25 (0.12)
Decimal points
Line through (0.5, 1.25) and (2.5, 0.25)
Slope
-1/2 (-0.5)
Same point twice
(2, 3) and (2, 3) do not define a line
Slope
—
Zero slope cannot fix x2
Find x2 with slope 0 has no unique answer
Slope
—
Frequently asked questions
What does undefined slope mean?+
Undefined slope means the line is vertical. The run is 0, and division by 0 is not defined, so the slope cannot be written as a number.
Is slope the same as rise over run?+
Yes. Rise over run is the visual way to describe slope: how far the line moves up or down divided by how far it moves left or right.
Can slope be negative?+
Yes. A negative slope means the line falls as you move from left to right. For example, a slope of -2 means the line goes down 2 units for every 1 unit to the right.
Which point should be point 1?+
Either point can be point 1. If you swap the two points, both the rise and run change signs, so the slope stays the same.
Can I find a missing coordinate if I know the slope?+
Yes. Choose Find missing y2 or Find missing x2. The calculator rearranges the slope formula to solve for the missing coordinate, then builds the full line from the solved point.
Why can't I find a unique x-coordinate when slope is 0?+
A slope of 0 is a horizontal line. If the y-value is the same, infinitely many x-values work; if the y-value is different, no point on that horizontal line has that y-value.
What is percentage grade?+
Percentage grade is slope multiplied by 100. It is commonly used for ramps, roads, trails, and roofs. A slope of 0.12 is a 12% grade, and the ADA ramp limit of 1:12 is an 8.33% grade.
How do I find the slope of a parallel or perpendicular line?+
A parallel line has exactly the same slope. A perpendicular line has the negative reciprocal: flip the fraction and change the sign, so the perpendicular to slope 3/2 has slope -2/3. The calculator shows both in the result panel.
What is the slope of a horizontal line versus a vertical line?+
A horizontal line has slope 0 because its rise is 0. A vertical line has undefined slope because its run is 0 and you cannot divide by 0. They are perpendicular to each other.
What does a slope of 1 mean?+
A slope of 1 means the line rises exactly 1 unit for every 1 unit it moves right, so it climbs at a 45° angle. That is a 100% grade. A slope of -1 falls at the same rate.
How do I convert an angle to a slope?+
Take the tangent of the angle of inclination: m = tan θ. For 30°, m = tan 30° ≈ 0.577. Going the other way, θ = arctan(m). Choose Slope from an angle and the calculator does both.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 6, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
References
- OpenStax, Elementary Algebra 2e, Section 3.4 “Understand Slope of a Line” — Rise over run, the slope formula, horizontal and vertical lines.
- OpenStax, Elementary Algebra 2e, Section 3.6 “Find the Equation of a Line” — Point-slope form and the slopes of parallel and perpendicular lines.
- U.S. Access Board, ADA Accessibility Standards, Chapter 4: Ramps and Curb Ramps (§405.2 Slope) — Ramp running slope not steeper than 1:12 (8.33%).
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Last updated: September 6, 2026