Angle of Elevation Calculator Feet and Degrees

This angle of elevation calculator helps you determine the angle in degrees between a horizontal line and a line of sight to a point above the horizontal. You can input the vertical rise in feet and get the angle of elevation in degrees.

What is Angle of Elevation?

The angle of elevation is the angle between a horizontal line and the line of sight to an object above the horizontal. It's commonly used in construction, surveying, and engineering to measure slopes and inclines.

For example, if you're looking at the top of a building from street level, the angle of elevation is the angle between the horizontal ground line and your line of sight to the top of the building.

How to Calculate Angle of Elevation

To calculate the angle of elevation, you need to know the vertical rise (the distance from the horizontal line to the point you're observing) and the horizontal distance (the distance from the observer to the point directly below the observed point).

The angle of elevation can be calculated using trigonometric functions. The most common method uses the arctangent function, which is the inverse of the tangent function.

Key Concept

The angle of elevation is always measured from the horizontal line upwards. It's an acute angle (less than 90 degrees) when looking upwards and an obtuse angle (greater than 90 degrees) when looking downwards.

Angle of Elevation Formula

The formula for calculating the angle of elevation (θ) is:

Angle of Elevation Formula

θ = arctan(vertical rise / horizontal distance)

Where:

θ = angle of elevation in degrees
vertical rise = the vertical distance from the horizontal line to the point (in feet)
horizontal distance = the horizontal distance from the observer to the point (in feet)

This formula uses the arctangent function to convert the ratio of vertical rise to horizontal distance into an angle in degrees.

Angle of Elevation Examples

Let's look at a couple of examples to see how the angle of elevation calculator works.

Example 1: Construction Slope

Suppose you're measuring the slope of a construction site. You measure a vertical rise of 10 feet and a horizontal distance of 20 feet. Using the angle of elevation formula:

Calculation

θ = arctan(10 / 20) = arctan(0.5) ≈ 26.565°

The angle of elevation is approximately 26.57 degrees.

Example 2: Surveying a Roof

When surveying a roof, you measure a vertical rise of 15 feet and a horizontal distance of 30 feet. Using the angle of elevation formula:

Calculation

θ = arctan(15 / 30) = arctan(0.5) ≈ 26.565°

The angle of elevation is approximately 26.57 degrees.

Angle of Elevation FAQ

What is the difference between angle of elevation and angle of depression?: The angle of elevation is the angle between the horizontal line and the line of sight to an object above the horizontal. The angle of depression is the angle between the horizontal line and the line of sight to an object below the horizontal.
When would I use an angle of elevation calculator?: You would use an angle of elevation calculator when you need to measure the slope or incline of a surface, such as a roof, hill, or construction site. It's also useful in surveying and engineering applications.
What units should I use with the angle of elevation calculator?: The angle of elevation calculator typically uses degrees for the angle and feet for the vertical rise and horizontal distance. You can convert other units to feet if needed.
Can the angle of elevation be greater than 90 degrees?: Yes, the angle of elevation can be greater than 90 degrees when looking downwards. In this case, it's often referred to as the angle of depression.
Is the angle of elevation the same as the pitch angle?: Yes, the angle of elevation is sometimes referred to as the pitch angle, especially in construction and engineering contexts. Both terms describe the angle between a horizontal line and a line of sight to an object above the horizontal.