Rise Over Run
Compute slope from rise and run inputs. Get simplified fraction, decimal, percentage grade, and angle in degrees. Free online algebra slope calculator for students and professionals.
About This Calculator
The Rise Over Run Calculator computes the slope of a line from the vertical change (rise) and horizontal change (run) between any two points. Slope is one of the most fundamental concepts in algebra and coordinate geometry, representing how steep a line is. Whether you are a student learning linear equations, a civil engineer planning road gradients, a carpenter building stairs, or a DIY enthusiast designing a ramp, this calculator provides all the key metrics you need from just two numbers.
The calculation is straightforward: slope = rise ÷ run. For example, if the rise is 6 units and the run is 3 units, the slope equals 6 / 3 = 2. The calculator presents this in four ways: as a simplified fraction (2/1), a decimal (2.00), a percentage grade (200%), and an angle in degrees (approximately 63.4 deg). Each representation serves a different purpose -- fractions are common in algebra textbooks, decimals are used in graphing, percentages are standard in road construction, and angles are useful in engineering and design.
The angle is derived using the inverse tangent function: theta = arctan(rise / run). A slope of 1 corresponds to a 45 deg angle, while a slope of 0 means the line is horizontal (0 deg), and a vertical line (run = 0) has an undefined slope with an angle of 90 deg.
Regional Notes
India: The National Building Code recommends a maximum ramp gradient of 1:12 (8.33%) for wheelchair access. Road gradients on Indian highways typically range from 3% to 6% depending on terrain classification.
US: The ADA requires a maximum slope of 1:12 for wheelchair ramps. The Interstate Highway System limits grades to a maximum of 6% in mountainous terrain and 3% in flat areas. Roof pitch in the US is commonly expressed as a ratio like 4:12 (4 inches of rise per 12 inches of run).
UK: Part M of the Building Regulations recommends a maximum ramp gradient of 1:20 (5%) for accessible entrances. Road gradients on motorways are generally limited to 3-4%. Stair regulations require a rise of 150-220 mm and a going (run) of 220-300 mm.
Frequently Asked Questions
How does the Rise Over Run calculator work?
The calculator divides the rise (vertical change) by the run (horizontal change) to compute the slope. It then shows the result as a simplified fraction, a decimal, a percentage grade, and the angle of incline in degrees. For example, a rise of 6 units and a run of 3 units gives a slope of 2 (fraction 2/1), a grade of 200%, and an angle of approximately 63.4 deg.
What is the rise over run formula?
The rise over run formula is slope = rise / run = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are any two points on the line. This ratio represents how many units the line goes up (rise) for every unit it moves horizontally (run).
What does a slope of 0 mean?
A slope of 0 means the line is horizontal -- there is no vertical change as x increases. The rise is zero while the run is positive, so the line is flat. A horizontal line has a grade of 0% and an angle of 0 deg.
What does an undefined slope mean?
An undefined slope occurs when the run (horizontal change) is zero, meaning the line is vertical. Since division by zero is mathematically undefined, the slope cannot be computed as a finite number. A vertical line has an infinite slope and an angle of 90 deg.
How is rise over run used in construction?
In construction, rise over run is used to calculate the pitch of roofs and the steepness of stairs. For stairs, the rise is the height of each step (riser) and the run is the depth of each step (tread). Building codes often require the sum of rise and run to be around 17-18 inches for safe stairs. Carpenters follow rules like rise + run = 18 inches or 2 x rise + run = 25 inches.
What is the difference between slope and grade?
Slope and grade both measure steepness but use different units. Slope is the ratio rise / run, often expressed as a fraction or decimal. Grade is the same ratio expressed as a percentage (slope x 100%). For example, a slope of 0.05 equals a grade of 5%, meaning the surface rises 5 units for every 100 units of horizontal distance. Grade is commonly used in road construction and civil engineering.
How do you convert slope to an angle in degrees?
To convert slope to an angle in degrees, use the inverse tangent (arctangent) function: angle = arctan(rise / run). The result is in degrees. For example, a slope of 1 (45% grade) gives an angle of 45 deg, and a slope of 0.577 gives an angle of 30 deg.
What is a good rise over run for a ramp?
For wheelchair ramps, the Americans with Disabilities Act (ADA) recommends a maximum slope of 1:12 (rise over run), which equals a grade of about 8.33% and an angle of approximately 4.76 deg. In the UK, Part M of Building Regulations recommends a maximum gradient of 1:20 (5%) for ramps. In India, the National Building Code recommends a maximum of 1:12 for wheelchair access.