Angle of Elevation Calculator

Compute the angle of elevation, slope, and hypotenuse using horizontal distance and height difference. Perfect for surveying, construction, and physics.

The horizontal length from observer to object (must be > 0).
The height difference (can be negative for depression).
10m / 5m (26.6°)
20m / 10m (26.6°)
5m / 5m (45°)
100m / 30m (16.7°)
15m / -5m (-18.4°)
Elevation Angle Results
1. Input Values
Horizontal Distance = 10.00 units
Vertical Height = 5.00 units
26.57°
Angle (degrees)
0.464 rad
Angle (radians)
50.0%
Slope (rise/run)
11.18
Hypotenuse (units)
2. Calculation Steps
tan(θ) = height / distance = 0.5
θ = arctan(height / distance) = 26.565°
3. Visual Representation

Right triangle representation: adjacent (horizontal), opposite (vertical), hypotenuse (line of sight).

Understanding Angle of Elevation

The angle of elevation is the angle formed between the horizontal line of sight and the line of sight up to an object. It is a fundamental concept in trigonometry with applications in surveying, navigation, architecture, and physics.

Mathematical Definition:

If you are looking at an object above you, the angle of elevation θ satisfies:

tan(θ) = opposite / adjacent = vertical height / horizontal distance

Therefore, θ = arctan( height / distance )

Key Relationships

Quantity Formula Description
Angle (degrees) θ° = arctan(height/distance) × 180/π Elevation angle in degrees
Slope percent (height/distance) × 100% Grade percentage
Hypotenuse √(distance² + height²) Line-of-sight distance
Height from angle height = distance × tan(θ) If angle known

Applications

1

Surveying & Mapping: Determine heights of buildings, mountains, or trees using distance and elevation angle.

2

Construction: Calculate slope of roads, ramps, or roofs (grade).

3

Physics / Ballistics: Trajectory angles and projectile motion.

4

Aviation: Glide slopes and approach angles.

Calculator Features:

  • Real-time calculation as you type (or click Calculate)
  • Handles positive (elevation) and negative (depression) angles
  • Interactive triangle diagram updates automatically
  • Displays degrees, radians, slope percentage, and hypotenuse
  • Step-by-step breakdown using arctan formula

Frequently Asked Questions

Angle of elevation is measured upward from the horizontal; angle of depression is measured downward. In this calculator, a negative height produces a negative angle (depression).

No, horizontal distance must be greater than zero (division by zero is undefined). The calculator will show an error if distance ≤ 0.

Slope percent = (vertical height / horizontal distance) × 100. For example, a 10% slope means a rise of 10 units per 100 units of horizontal distance.

Any consistent unit (meters, feet, etc.). The calculator treats them as pure numbers, so the angle is independent of units as long as both inputs use the same unit.

The triangle is scaled to fit the canvas; proportions are preserved so the angle visually matches the computed value. Very large or small ratios may be truncated but angle remains correct.