Height Distance Calculator

Welcome to the Height Distance Calculator! This tool is designed to help you measure heights and distances without climbing tall objects or relying on guesswork. Whether you’re trying to estimate the height of a tree, calculate your distance from a building, or even figure out how far you can see to the horizon, this calculator makes the math quick and simple.

Just enter the distance, angle, or observer height, and the calculator does the rest. You can start using it right away or keep reading to learn more about the formulas, parameters, and step-by-step examples.

Understanding the Formula

There are three main formulas that the Height Distance Calculator uses, depending on what you want to measure:

1. Calculating an Object’s Height
If you want to find how tall something is (like a tower):
Object Height = (Distance to Base × tan(Angle of Elevation)) + Observer Height

2. Calculating Distance to an Object
If you already know the object’s height:
Distance = Height of Object / tan(Angle of Depression)

3. Calculating Distance to the Horizon
If you want to know how far you can see:

• Distance (miles) = 1.22 × √Observer Height (feet)
• Distance (km) = 3.57 × √Observer Height (meters)

Each formula uses simple trigonometry or geometry, so the calculator saves you from doing the math by hand.

Parameters Explained

Distance to Base
The horizontal ground distance between you and the object. Measured in meters or feet.

Angle of Elevation
The angle from your line of sight up to the top of the object. Measured in degrees.

Observer Height
Your eye level above the ground. This ensures calculations are realistic and accurate.

Height of Object
The known height of the object, often used when calculating your distance from it.

Angle of Depression
The angle from the top of the object downward to your position. Measured in degrees.

Earth’s Radius
For horizon calculations, the Earth’s radius is used (about 6,371 km or 3,959 miles).

How to Use the Height Distance Calculator — Step-by-Step Example

Let’s try calculating the height of a building:

• Distance to Base = 50 meters
• Angle of Elevation = 40°
• Observer Height = 1.7 meters

Step 1: Apply the formula
Height = (50 × tan(40°)) + 1.7

Step 2: Solve
tan(40°) ≈ 0.839
Height = (50 × 0.839) + 1.7 = 41.95 + 1.7 = 43.65 meters

Final Result: The building is approximately 43.7 meters tall.

Now let’s try a horizon example:
If you are standing on a cliff 100 feet high, the distance to the horizon is:
Distance = 1.22 × √100 = 1.22 × 10 = 12.2 miles

So, you could see about 12 miles into the distance.

Additional Information

Here’s a quick reference for horizon distances at common observer heights:

FAQs