Angle in Degrees
Angle in Radians
Vertical Rise
Horizontal Distance
Line of Sight
Slope Grade
Rise : Run Ratio
Choose a solving mode, enter known measurements, and calculate the elevation angle in degrees.
This graph shows how angle changes as horizontal distance varies while the current rise remains fixed.
The highlighted point represents your latest submitted result.
Each new calculation is stored in the table below and can be exported as CSV or PDF.
| # | Mode | Rise (m) | Run (m) | Hypotenuse (m) | Angle (deg) | Grade (%) | Timestamp |
|---|---|---|---|---|---|---|---|
| No calculations yet. Submit the form to create history entries. | |||||||
These sample cases show common right-triangle angle-of-elevation situations.
| Scenario | Rise | Run | Angle | Notes |
|---|---|---|---|---|
| Small lab setup | 3 m | 8 m | 20.5560° | Moderate viewing incline. |
| Survey tripod reading | 12 ft | 30 ft | 21.8014° | Useful for field verification. |
| Roofline observation | 7 m | 14 m | 26.5651° | Rise is half the run. |
| Tower sighting | 25 m | 40 m | 32.0054° | Steeper angle than the roofline case. |
These are the relationships used by the calculator for different known inputs.
tan(θ) = rise ÷ run
θ = atan(rise ÷ run)
rise = target height - observer height
θ = atan((target height - observer height) ÷ run)
cos(θ) = run ÷ hypotenuse
θ = acos(run ÷ hypotenuse)
sin(θ) = rise ÷ hypotenuse
θ = asin(rise ÷ hypotenuse)
The calculator converts all length values to meters before solving. Degree output is obtained from the radian result using θdeg = θrad × 180 ÷ π.
Follow these steps for a consistent and valid angle-of-elevation result.
- Select the solving mode that matches the measurements you already know.
- Enter the required values and choose the correct unit for each field.
- Pick how many decimal places you want displayed in the results.
- Press Calculate to show the result above the form.
- Review the degree value, radian value, grade percentage, and line-of-sight length.
- Check the Plotly graph to see how distance affects angle for the same rise.
- Use the CSV or PDF buttons to export recent calculation history.
These answers cover common classroom, lab, and field usage questions.
What is the angle of elevation?
It is the angle measured upward from a horizontal line to an object above the observer. In a right triangle, it links vertical rise and horizontal distance.
Which formula does this calculator use?
The main relation is tan(θ) = rise ÷ run. The tool also uses asin and acos when line-of-sight length is supplied instead of one side.
Why are degrees shown instead of only radians?
Degrees are easier for fieldwork, classroom problems, and quick interpretation. The calculator also shows radians for technical comparison and verification.
Can I use different units for height and distance?
Yes. Each value is converted internally to meters first. That allows mixed-unit input while keeping the angle result mathematically consistent.
What happens if the target is below the observer?
The result becomes negative, which indicates an angle of depression rather than elevation. The calculator labels that condition clearly.
When should I use the line-of-sight modes?
Use them when you know the slanted viewing distance from an instrument, cable, or sensor path and one other triangle side.
Does this assume level ground?
Yes. The standard formulas assume a horizontal reference line and a right-triangle geometry. Uneven ground requires adjusted surveying methods.
What do the graph and history table show?
The graph shows how the angle changes as horizontal distance varies for the current rise. The history table stores recent calculations for export.