geo-distance Verified Precision Tool
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 EllipsoidPoint 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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