Slope Grade & Ratio Calculator

Slope Grade & Ratio Calculator

Use the Slope Grade & Ratio Calculator to calculate or convert a slope using the information you already know.

You can start with:

• Rise and run
• Percent grade
• Angle in degrees
• Slope ratio

The calculator immediately converts your input into equivalent slope values such as percent grade, degrees, vertical-to-horizontal ratio, horizontal-to-vertical ratio, slope length, millimetres per metre, and inches per foot.

It also supports mixed units, so your rise and run do not have to use the same measurement unit.

Calculate Slope From Rise and Run

The most common way to calculate a slope is from its rise and run.

Rise is the vertical change.

Run is the horizontal distance.

The basic relationship is:

Slope = Rise ÷ Run

Percent grade is then calculated as:

Grade % = (Rise ÷ Run) × 100

For example, if a surface rises 1 foot over a horizontal run of 12 feet:

1 ÷ 12 × 100 = 8.33%

So the slope has a grade of approximately:

8.33%

The calculator also converts that same slope into an angle and ratio automatically.

What Is Percent Grade?

Percent grade expresses vertical change as a percentage of horizontal distance.

A:

1% grade

means the surface rises or falls 1 unit vertically for every 100 units of horizontal run.

Similarly:

5% grade = 5 units vertical for every 100 units horizontal

Percent grade is commonly used for:

• Driveways
• Drainage
• Landscaping
• Roads
• Site grading
• Ramps
• Pipe runs
• Paving

Slope Percentage to Degrees

Slope percentage and slope angle describe the same steepness in different ways.

To convert percent grade to degrees:

Angle = arctan(Grade ÷ 100)

For example:

5% grade ≈ 2.86°

The calculator performs this conversion automatically and avoids the need to use trigonometric formulas manually.

Degrees to Percent Grade

You can also convert an angle into percent grade.

The relationship is:

Grade % = tan(Angle) × 100

For example:

10° ≈ 17.63% grade

Enter the angle into the calculator and all equivalent slope formats will be shown instantly.

Slope Ratio Calculator

Slope ratios are commonly written in formats such as:

1:12

or:

12H:1V

These describe the relationship between vertical and horizontal change.

For example:

1:12

means:

1 unit vertical for every 12 units horizontal

The same slope can also be written:

12H:1V

Because ratio conventions vary between industries and calculators, this tool always identifies the direction of the ratio.

1:12 Slope in Percent and Degrees

A 1:12 slope means one unit of vertical change for every twelve units of horizontal run.

The decimal slope is:

1 ÷ 12 = 0.08333

Percent grade:

0.08333 × 100 = 8.33%

Angle:

arctan(1 ÷ 12) ≈ 4.76°

So approximately:

1:12 = 8.33% = 4.76°

This calculator can perform the same conversion for other ratios such as 1:20, 1:50, or custom values.

Convert Between Slope Formats

A single slope can be represented in several equivalent formats.

For example, one slope might be shown as:

Grade: 5% Angle: 2.86° Ratio: 1:20 Horizontal : Vertical: 20H:1V Millimetres per metre: 50 mm/m Inches per foot: 0.60 in/ft

The calculator converts between these formats automatically.

Mixed Rise and Run Units

Rise and run do not need to use the same unit.

For example, you can calculate a slope using:

Rise: 6 inches

and:

Run: 12 feet

The calculator converts both values internally before calculating the slope.

Supported units include:

• Millimetres
• Centimetres
• Metres
• Inches
• Feet

This is useful when measurements come from different plans, tools, or field notes.

Calculate Rise From Grade and Run

If you know the grade and horizontal distance, you can calculate the required rise or fall.

The formula is:

Rise = Run × (Grade ÷ 100)

For example:

2% grade over 30 m

gives:

30 × 0.02 = 0.6 m

So the vertical change is:

0.6 m

or:

600 mm

The calculator's Fall or Rise Over a Distance section performs this automatically.

Calculate Run From Grade and Rise

If you know the grade and vertical change, you can solve for the required horizontal run.

The formula is:

Run = Rise ÷ (Grade ÷ 100)

This is useful when planning a slope where the vertical change is fixed but you need to determine the required horizontal distance.

Calculate Rise From Angle and Run

If the angle and horizontal run are known:

Rise = Run × tan(Angle)

The calculator can solve this automatically when you enter an angle and a known run.

Calculate Run From Angle and Rise

If the rise and angle are known:

Run = Rise ÷ tan(Angle)

This allows the same calculator to work as a reverse slope calculator rather than requiring a separate tool.

Calculate Rise or Run From a Ratio

A slope ratio can also be used to solve missing dimensions.

For a 1:12 slope:

Rise = Run ÷ 12

For example:

12 ft run → 1 ft rise

Likewise:

24 ft run → 2 ft rise

The calculator can also work backward when the rise is known.

What Is Slope Length?

Slope length is the true distance along the inclined surface rather than the horizontal run.

It is calculated using:

Slope Length = √(Rise² + Run²)

This can be useful when estimating materials for:

• Ramps
• Driveways
• Landscaping
• Roofing
• Walkways
• Site work

The calculator displays slope length whenever enough dimensional information is available.

What Does mm per Metre Mean?

Millimetres per metre, often written mm/m, describes vertical change over one horizontal metre.

For example:

20 mm/m

means the surface changes vertically by 20 mm for every 1 metre of horizontal distance.

This is equivalent to:

2% grade

because:

20 ÷ 1000 × 100 = 2%

Inches per Foot

Slope may also be expressed as vertical inches per horizontal foot.

For example:

0.24 in/ft

means the surface changes by 0.24 inches for every 12 inches of horizontal run.

This format can be useful for construction and drainage measurements using imperial units.

Calculate Fall Over a Distance

For drainage and grading work, users often know the required percentage and need to determine the total fall.

For example:

2% slope over 30 m

produces:

0.6 m fall

which is also:

600 mm

The calculator can display the result in both the selected unit and useful secondary units.

Positive and Negative Slopes

A slope may rise or fall.

A positive slope represents an upward change.

A negative slope represents a downward change.

Instead of requiring users to understand signed mathematics, the calculator also provides clear:

Rise ↑

and:

Fall ↓

controls.

This makes downhill calculations easier to understand while still supporting negative input values.

Why Rise and Run Must Use the Same Base Unit

The slope itself is unitless because it is a ratio of two distances.

However, the rise and run must represent comparable physical measurements.

This calculator handles that automatically by converting mixed units internally before performing the calculation.

For example:

6 inches rise / 12 feet run

is converted to equivalent units before calculating the grade.

Common Slope Applications

Drainage

Useful outputs include:

• Percent grade
• Fall over distance
• mm per metre
• Rise or fall

Ramps

Commonly useful values include:

• Ratio
• Grade percentage
• Angle
• Required run
• Slope length

Driveways

Useful values include:

• Percent grade
• Angle
• Total rise or fall

Landscaping

Slope calculations can help with:

• Grading
• Drainage
• Paths
• Retaining areas
• Ground shaping

Construction and Site Work

Contractors may use slope calculations when checking:

• Elevation differences
• Finished grades
• Site drainage
• Access routes
• Paving
• Earthworks

Slope Grade vs Slope Angle

Percent grade and angle measure the same slope but use different scales.

A 100% grade does not mean a 90° slope.

A 100% grade means:

Rise = Run

which corresponds to:

45°

This distinction is important when converting between percentage and degrees.

Is a 50% Grade Equal to 50 Degrees?

No.

A 50% grade means:

Rise ÷ Run = 0.5

The corresponding angle is approximately:

26.57°

Percent grade and degrees are not interchangeable numbers.

Frequently Asked Questions

How do I calculate slope from rise and run?

Divide rise by run. Multiply the result by 100 to get percent grade.

Grade % = Rise ÷ Run × 100

What is the difference between grade and slope?

Slope is the underlying rise-to-run relationship. Grade usually expresses that slope as a percentage.

How do I convert slope percentage to degrees?

Use:

Angle = arctan(Grade ÷ 100)

The calculator does this automatically.

How do I convert degrees to slope percentage?

Use:

Grade % = tan(Angle) × 100

What does a 1:12 slope mean?

It means one unit of vertical change for every 12 units of horizontal distance.

What is a 1:12 slope in percent?

Approximately 8.33%.

What is a 1:12 slope in degrees?

Approximately 4.76°.

Can rise and run use different units?

Yes. This calculator automatically converts supported mixed units before calculating the slope.

How do I calculate fall over a distance?

Multiply the horizontal distance by the decimal grade.

For a 2% grade:

Distance × 0.02 = Fall

How do I calculate slope length?

Use the Pythagorean theorem:

√(Rise² + Run²)

Does this calculator support downward slopes?

Yes. You can select Fall ↓ or enter a negative rise, grade, or angle.

Is this calculator a building-code compliance checker?

No. It calculates geometric slope values only. Requirements for ramps, drainage, driveways, roofs, or other construction work can vary by project and jurisdiction, so applicable plans, codes, and professional requirements should be checked separately.

Related Calculations to Internally Link

For this page, the strongest future internal-link opportunities are:

• Rise Over Run Calculator
• Slope Percentage Calculator
• Grade to Degrees Calculator
• Degrees to Grade Calculator
• 1:12 Slope Calculator
• Fall Over Distance Calculator
• Ramp Slope Calculator
• Roof Pitch Calculator
• Gradient Calculator
• Distance Calculator