Description
Calculate CEP50 for a zero-mean isotropic Gaussian horizontal-error model.
Geodesy distinguishes a mathematical reference ellipsoid, a realized coordinate datum and the physical gravity field. Geodetic latitude follows the ellipsoid normal; geocentric latitude follows a radius from the center. Ellipsoidal height, orthometric height and geoid undulation are separate signed quantities. Keep the declared ellipsoid, coordinate axes, angular units and time scale with a result.
Calculate CEP50 for a zero-mean isotropic Gaussian horizontal-error model.
When to use this tool
Use this tool when you need to calculate CEP50 for a zero-mean isotropic Gaussian horizontal-error model.
How to use the tool and how it works
- Enter isotropicSigmaMeters using the definitions below.
- Run the operation. Resolve input-format errors before interpreting an output.
- Read result.cep50Meters, result.degenerate, using the stated boundary, ordering, sign and absence conventions.
Calculate sigma×sqrt(2 ln 2) as a 50% circular radius for the stated zero-mean isotropic Gaussian horizontal-error model. Mark sigma=0 as degenerate.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| isotropicSigmaMeters | Common east/north one-axis Gaussian standard deviation in meters, zero through 10⁷. | Finite numeric value satisfying the stated comparisons. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.cep50Meters | 50%-coverage circle radius for the stated zero-mean isotropic Gaussian model, in meters. |
| result.degenerate | Operation-specific degenerate case: near-zero cone constant or zero isotropic sigma, as described above. |
{
"input": {
"isotropicSigmaMeters": 1
},
"output": {
"result": {
"cep50Meters": 1.1774100225154747,
"degenerate": false
}
}
}Limitations and assumptions
- Sigma is the common one-axis standard deviation in meters, from zero through 10⁷. The formula does not apply unchanged to biased, anisotropic or non-Gaussian horizontal errors.
- All quantities are finite and retain the units stated for this operation. Ellipsoid-parameter tools use semi-major axis 1–10⁸ m and dimensionless flattening 0–0.02; explicit-axis tools use 0.9a≤b≤a unless a tighter bound is stated. These tools do not fetch datums, geoid grids, satellite observations or Earth-orientation updates.
- Every declared outer field is required and unknown outer fields are rejected. Strings and JSON text have size limits, lists are bounded to 128 entries, and JSON nesting/node counts are bounded. Tighter operation-specific bounds stated above take precedence.
- Numeric results must be finite. Large physical magnitudes are allowed by the output evidence checks, while integer fields and source schemas retain their exactness rules. Source indexes are zero-based. Floating-point residues can remain even where an ideal formula gives an exact zero.
Alternative or Complementary methods
Use a coordinate transform for a change of representation and explicit datum parameters for a change of reference frame. Preserve model and convergence metadata, and use observation and datum information appropriate to a real survey before interpreting a computed tolerance as accuracy.
References
Similar or alternative tools
- 2DRMS Horizontal Accuracy Estimate Calculator
Calculate 2DRMS from horizontal standard deviations and report Gaussian coverage only for the stated isotropic case.
- Dilution of Precision DOP Geometric Factor Classifier
Classify supplied DOP using this tool’s illustrative thresholds and policy labels.