Earth Centered Earth Fixed Coordinate Calculator

Calculator

Formula Used

Geodetic to ECEF

Let latitude be φ, longitude be λ, height be h, semi-major axis be a, and flattening be f.

f = 1 / inverse flattening

e² = 2f - f²

N = a / √(1 - e² sin²φ)

X = (N + h) cosφ cosλ

Y = (N + h) cosφ sinλ

Z = (N(1 - e²) + h) sinφ

ECEF to Geodetic

The reverse mode uses Bowring style starting values and short iteration.

p = √(X² + Y²)

λ = atan2(Y, X)

θ = atan2(Za, pb)

φ = atan2(Z + e'²b sin³θ, p - e²a cos³θ)

h = p / cosφ - N

How to Use This Calculator

1. Select the conversion mode.
2. Choose the reference ellipsoid.
3. Select meters or kilometers for linear values.
4. Enter latitude, longitude, and height for forward conversion.
5. Enter X, Y, and Z for reverse conversion.
6. Set decimal places for the final output.
7. Press the calculate button.
8. Use the CSV or PDF buttons to save the result.

Example Data Table

About Earth Centered Earth Fixed Coordinates

Why this coordinate frame matters

Earth centered earth fixed coordinates give each point a position from the center of the planet. The x axis passes through the equator at zero longitude. The y axis passes through the equator at ninety degrees east. The z axis follows the north polar axis. This frame is useful because it turns curved latitude and longitude data into a three dimensional Cartesian point.

Geodetic input values

A geodetic position uses latitude, longitude, and ellipsoidal height. Latitude is measured from the equator. Longitude is measured from Greenwich. Height is measured above or below the chosen reference ellipsoid. The calculator uses the ellipsoid shape to find the prime vertical radius. That radius changes with latitude, because the earth is flattened at the poles.

Forward conversion uses

The forward method is often used in surveying, GNSS logging, GIS import tools, and satellite checks. It is also useful before calculating straight line distance, local tangent vectors, or rotation matrices. Small changes in ellipsoid selection can change the final coordinates. That is why this tool lets you set WGS84, GRS80, Airy 1830, or a custom body.

Reverse conversion notes

Reverse solving starts with x, y, and z. The tool estimates longitude from atan2. It then iterates latitude and height until the solution is stable. This approach handles typical terrestrial points well. It also reports radius length and geocentric latitude, so you can compare the returned position with the raw Cartesian direction.

Precision and exports

Precision matters in coordinate work. A meter level output may be enough for maps. Millimeter level output may be needed for engineering checks. The decimal control lets you match the result to your source data. Export buttons help keep records for later review. The CSV file is useful for spreadsheets. The PDF report is useful for sharing a single result.

Best practice

Use consistent units and signs. North latitude is positive. East longitude is positive. West longitude is negative. Heights may be negative below the ellipsoid. Always confirm that your source datum matches the selected ellipsoid. Mixing datums can create position shifts, even when the formulas are correct. For serious field work, treat this calculator as a transparent checking tool. Verify final coordinates with official survey software when legal boundaries, navigation safety, or critical infrastructure depend on the output. Document every assumption before final use.

FAQs

What does ECEF mean?

ECEF means Earth Centered Earth Fixed. It is a Cartesian coordinate frame fixed to the rotating earth. It gives X, Y, and Z values from the earth center.

Which ellipsoid should I choose?

WGS84 is a common choice for GPS and global mapping. GRS80 is close to WGS84. Airy 1830 is useful for some older British mapping contexts.

Can I use negative longitude?

Yes. East longitude is positive. West longitude is negative. For example, New York uses a negative longitude value.

Can height be negative?

Yes. Ellipsoidal height can be negative when the point is below the selected reference ellipsoid.

Is geocentric latitude the same as geodetic latitude?

No. Geodetic latitude uses the ellipsoid normal. Geocentric latitude uses the line from the earth center to the point.

Why do results change with ellipsoid choice?

Each ellipsoid has a different shape. The semi-major axis and flattening change the radius used in the coordinate equations.

Does this calculator handle kilometers?

Yes. Select kilometers in the unit field. The tool converts internally and displays matching output values.

Can I export the result?

Yes. After calculation, use the CSV button for spreadsheet data. Use the PDF button for a simple report.