Description
Return that central angle in radians and its fraction of a full 2π turn.
Spherical geography models Earth with one radius and angular coordinates. Surface arcs, polar heights, circle radii, and area fractions are different derived quantities; an ideal spherical result does not include ellipsoid or terrain effects.
Return that central angle in radians and its fraction of a full 2π turn.
When to use this tool
Use Spherical Distance Central Angle Reference when you need a stated spherical geographic term or angular conversion.
How to use the tool and how it works
- Enter distance, radius. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read centralAngle, fractionOfCircumference. Use the output convention below.
Require nonnegative distance and positive radius, with distance divided by radius no greater than π. Return that central angle in radians and its fraction of a full 2π turn.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| distance | Distance in the stated common unit and geometric model. | Required. Finite number; minimum 0. |
| radius | Radius in the common length unit, with its geometric role defined above. | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| centralAngle | Central Angle | Required. Finite number. |
| fractionOfCircumference | Fraction Of Circumference | Required. Finite number. |
{
"input": {
"distance": 3.141592653589793,
"radius": 2
},
"output": {
"centralAngle": 1.5707963267948966,
"fractionOfCircumference": 0.25
}
}Limitations and assumptions
- Distance and radius must share units. The domain models a shortest spherical arc up to half a circumference; no point coordinates or ellipsoid are used.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use ellipsoidal geodesy or a suitable terrain model when spherical assumptions are inadequate. Keep angular units, physical length units, latitude definition, and reference radius explicit.
References
Similar or alternative tools
- Meridian Distance Latitude Sensitivity
Return signed meridian distance radius times latitude and derivative equal to radius.
- Pole Distance From Latitude
Return 90 minus latitude for the north pole or 90 plus latitude for the south pole.