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Earth Radius by Latitude Calculator

Calculate the exact WGS-84 ellipsoidal Earth radius at any specified latitude.

📍 Select World Location Presets or Custom Coordinates

WGS-84 Ellipsoid
Point 1 Coordinates (Origin)
Calculated Geodetic Solution
6369.0827 km (6369082.68 m)
Radius in Kilometers6369.0827 km
Radius in Meters6369082.68 m
🗺️ Interactive Geographic Map & Geodesic Trajectory

Click anywhere on the map or drag pins to update coordinates live.

Map Data: © OpenStreetMap ContributorsWGS-84 Precision Geodesic Curve

Step-by-Step Mathematical Derivation

1. Given Input Coordinates:
  • Latitude: 40.7128°
2. Model & Ellipsoid Reference:WGS-84 / Earth Sphere R = 6,371 km
3. Governing Geodesic Formula:R(φ) = sqrt([ (a²cosφ)² + (b²sinφ)² ] / [ (acosφ)² + (bsinφ)² ])
4. Variable Substitution:a = 6,378.137 km (equator), b = 6,356.752 km (poles)
5. Interpretation & Practical Application:

At latitude 40.7128°, Earth's WGS-84 ellipsoidal radius is 6369.0827 km.

Mathematical Formula

R(φ) = sqrt([ (a²cosφ)² + (b²sinφ)² ] / [ (acosφ)² + (bsinφ)² ])

Overview & Explanation

Calculates local WGS-84 ellipsoid radius, which varies from 6,378.137 km at the equator to 6,356.752 km at the poles.

How It Works

  • Evaluates geocentric radius of oblate spheroid at angle φ.

Practical Applications

  • Geodetic survey calibrations.
  • Gravitational acceleration adjustments.

Worked Example: Radius at 45° Latitude

Find Earth radius at mid-latitude.

1

Compute Radius

Evaluate WGS-84 formula

= 6,367.418 km (6,367,418 meters)

Frequently Asked Questions

Why is Earth radius smaller at the poles?
Earth centrifugal rotation causes equatorial bulging, making equatorial radius ~21 km larger than polar radius.

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