Examples
Examples
Try the starting example
- Physical size (chosen length unit)
- 10
- Angular size (arcseconds)
- 30
- Small-angle distance (same length unit)
- 68,754.935416
- Exact tangent-plane distance (same unit)
- 68,754.935294
- Relative approximation difference (%)
- 0
Try another scenario
- Physical size (chosen length unit)
- 11
- Angular size (arcseconds)
- 30
- Small-angle distance (same length unit)
- 75,630.428957
- Exact tangent-plane distance (same unit)
- 75,630.428824
- Relative approximation difference (%)
- 0
Calculation method
Calculation method
Small-angle distance (same length unit)
Small-angle distance=linearSize/angle; exact planar full-width geometry distance=linearSize/(2tan(angle/2)).
Exact tangent-plane distance (same unit)
Small-angle distance=linearSize/angle; exact planar full-width geometry distance=linearSize/(2tan(angle/2)).
Relative approximation difference (%)
Small-angle distance=linearSize/angle; exact planar full-width geometry distance=linearSize/(2tan(angle/2)).
Symbols and units
- a
- Physical size (chosen length unit)
- b
- Angular size (arcseconds)
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions & limits
Assumptions & limits
- Small-angle approximation, maximum angle one degree. Supported limits: All required fields must be finite values of the exact declared type and within displayed bounds. Lists contain1–1000 finite numbers. JSON tables are numeric rectangular rows, at most100 rows and30 columns; individual tools have stricter shape/domain constraints. Small-angle approximation, maximum angle one degree.
Are these inputs private?
These calculations run in your browser. A shared link contains the values you choose to share. Only questions submitted to the separate AI finder are sent to OpenAI.