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Geocentric vs Geodetic Latitude Converter

Converts between geocentric and geodetic latitude using the reference ellipsoid parameters.

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How to use this calculator

Inputs

Geodetic latitude (the ellipsoid normal) ⇄ geocentric latitude (the radius to the centre), on the ellipsoid surface or at a height.

Decimal degrees (−31.95), DMS (31 57 0 S) or DDM (31° 57.0′ S).

Ellipsoid
More options

Leave blank for the surface of the ellipsoid. A height uses the position's true direction from the centre (WGS84 or GRS80 only).

Enter the values and press Calculate.

Or load an example to see a worked result.

Normal (φ) and radius (θ) at your latitude
Not to scale — flattening exaggerated
Normal (φ) and radius (θ) at your latitudeQuarter of the ellipse in the meridian plane with the polar axis, the equatorial axis, a surface point, its normal and its radius.Equator (p)Polar axis (Z)φθφ (geodetic)θ (geocentric)Surface: tan θ = (1 − e²) tan φ
The ellipsoid normal (geodetic φ) and the radius to the centre (geocentric θ) are different directions except at the equator and the poles.

Batch from CSV

One row per calculation, with a header row. Values use the units currently selected in the form above. Up to 10,000 rows; nothing is uploaded.

How the method works

A fixed worked example to explain the method — it is not your result.

Geodetic normal and geocentric radius are different directions
Illustrative method
Geodetic normal and geocentric radius are different directionsQuarter of the ellipse in the meridian plane with the polar axis, the equatorial axis, a surface point, its normal and its radius.Equator (p)Polar axis (Z)φθφ (geodetic)θ (geocentric)Surface: tan θ = (1 − e²) tan φ
The ellipsoid normal (geodetic φ) and the radius to the centre (geocentric θ) are different directions except at the equator and the poles.

Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.

How to use this calculator

  1. Choose the direction: geodetic φ → geocentric θ, or θ → φ.
  2. Enter the latitude and choose WGS84, GRS80 or a custom flattening.
  3. Leave the height blank for the surface of the ellipsoid. Enter an ellipsoidal height to use the position's true direction from the centre (advanced).
  4. Press Calculate. Read both latitudes, the difference in arcseconds and which model was used.

How it works

Surface model: θ = atan2((1 − e²) sin φ, cos φ), with e² = f(2 − f); the reverse is φ = atan2(sin θ, (1 − e²) cos θ).

Height-aware model: the point is converted to X, Y, Z and θ = atan2(Z, √(X² + Y²)). Above the surface θ moves towards φ. The reverse is solved by bracketed bisection, which is guaranteed to converge because θ increases steadily with φ.

Geodetic latitude is the angle of the ellipsoid normal (what maps and GNSS use); geocentric latitude is the angle of the line to the Earth's centre.

Worked example

45° geodetic on WGS84, surface. θ = 44.80757678°, so φ − θ = 692.7236″ (about 0.1924°). Reversing returns 45° to better than 1×10⁻¹⁰°.

Common mistakes

  • Applying the surface formula to a satellite or aircraft. Enter the height: the surface formula is only right at h = 0.
  • Confusing geocentric latitude with reduced (parametric) latitude, which uses 1 − f instead of 1 − e².
  • Expecting a difference at the equator or poles — both latitudes agree exactly there.

Frequently asked questions

What's the difference?

Geodetic latitude is measured from the ellipsoid normal (what maps use); geocentric is measured from the Earth's centre. On the surface they differ by up to about 0.19°, near 45°.

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Cite this tool

Zerdly. (2026). Geocentric vs Geodetic Latitude Converter. Retrieved from https://www.zerdly.com/tools/geocentric-vs-geodetic-latitude-converter/

Tip: Enter any known values to calculate the remaining results.

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