Description
Return semimajor divided by the square root of 1 minus eccentricitySquared times sine-squared latitude.
An oblate reference ellipsoid describes its shape through semiaxes, flattening, and eccentricity. Curvature varies with geodetic latitude, and prime-vertical and meridional radii describe different local directions.
Return semimajor divided by the square root of 1 minus eccentricitySquared times sine-squared latitude.
When to use this tool
Use Ellipsoid Prime Vertical Radius Term when you need an ellipsoid-shape crosswalk or local curvature term.
How to use the tool and how it works
- Enter semimajor, eccentricitySquared, latitudeRadians. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read radius. Use the output convention below.
Require positive semimajor, eccentricitySquared within [0, 1), and latitudeRadians within ±π/2. Return semimajor divided by the square root of 1 minus eccentricitySquared times sine-squared latitude.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| semimajor | Semimajor | Required. Finite number; strictly above 0. |
| eccentricitySquared | Dimensionless squared eccentricity in [0, 1). | Required. Finite number; minimum 0; strictly below 1. |
| latitudeRadians | Geodetic latitude in radians. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| radius | Prime-vertical radius of curvature in the semimajor length unit. | Required. Finite number. |
{
"input": {
"semimajor": 10,
"eccentricitySquared": 0.36,
"latitudeRadians": 1.5707963267948966
},
"output": {
"radius": 12.5
}
}Limitations and assumptions
- This is the prime-vertical radius of curvature at geodetic latitude, in the semimajor length unit. Supply squared eccentricity rather than eccentricity or inverse flattening; no reference ellipsoid is selected.
- 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
Choose a named reference ellipsoid and a complete geodetic method for position or distance work. Distinguish eccentricity from its square and flattening from inverse flattening.
References
Similar or alternative tools
- Ellipsoid Meridional Radius Term
Return semimajor times (1-e²) divided by (1-e² sin² latitude) to the power 3/2.
- Oblate Spheroid Flattening Eccentricity Crosswalk
Return eccentricity squared f times (2-f), and its nonnegative square root for eccentricity.