WGS84 to Arc 1960 Converter
About WGS84 Coordinate System
WGS84 (World Geodetic System 1984) is the global standard geodetic reference system used by GPS. It defines an Earth-centered, Earth-fixed coordinate system and geodetic datum.
Developed by the U.S. Department of Defense in 1984, WGS84 has undergone several refinements (WGS84(G730), WGS84(G873), WGS84(G1150), WGS84(G1762)) to improve accuracy through GPS satellite observations.
WGS84 is the default coordinate system for GPS receivers worldwide. It is used in aviation, maritime navigation, Google Maps, OpenStreetMap, GIS applications, and scientific research.
WGS84 is the native coordinate system of the Global Positioning System (GPS), ensuring direct compatibility with all GPS receivers and satellite navigation systems worldwide.
As the most widely adopted geodetic datum, WGS84 provides a consistent global reference frame for mapping, surveying, and geospatial data exchange across international boundaries.
With continuous refinements, WGS84 achieves centimeter-level accuracy globally, making it suitable for high-precision applications like surveying, drone navigation, and scientific research.
About Arc 1960 Coordinate System
Arc 1960 is a historic geodetic datum used in East and Central Africa, covering countries including Kenya, Tanzania, Uganda, Burundi, and Rwanda. It uses the Clarke 1880 ellipsoid (a=6378249.145m, 1/f=293.465) and requires 7-parameter Helmert transformation for accurate conversion to WGS84. Arc 1960 was established as a refinement of the earlier Arc 1950 system.
Arc 1960 was established in 1960 as an updated adjustment of the Arc 1950 geodetic network, incorporating additional survey measurements and improved computation methods. It provided better accuracy for the growing mapping needs of East and Central African countries following independence.
Arc 1960 is still found in legacy mapping, historical cadastral surveys, and older infrastructure projects across East and Central Africa, particularly in Kenya, Tanzania, Uganda, Burundi, and Rwanda.
Arc 1960 served as a refined geodetic datum for East and Central Africa, improving upon Arc 1950 with additional survey observations for better accuracy.
Arc 1960 to WGS84 conversion requires a 7-parameter Helmert transformation. Parameters vary by country and region. Consult local surveying authorities for official values.
⚙️ 7-Parameter Helmert Transformation Guide
The 7-parameter Helmert transformation (also known as the 7-parameter similarity transformation / 3D conformal transformation) is the standard geodetic method for converting coordinates between two different datums. It applies three translations (dx, dy, dz), three rotations (rx, ry, rz), and one scale factor (s) to transform coordinates from one reference frame to another. This method preserves shapes (conformal) while shifting and rotating the entire coordinate system in 3D space.
WGS84 uses a different ellipsoid and reference frame than Arc 1960. To bridge this difference, a 7-parameter transformation is required. Unlike simpler methods such as geocentric translation (3-parameter) or Molodensky transformation, the 7-parameter Helmert provides the highest accuracy by accounting for all spatial differences between the two datums, including axis rotations and scale variations. The parameters must be sourced from local surveying authorities or geodetic organizations.
Translation Parameters
dx, dy, dz (meters) - shifts along X, Y, Z axes of the Earth-centered reference frame
Rotation Parameters
rx, ry, rz (radians) - rotations around each axis to align datum orientations
Scale Parameter
s (ppm) - scale factor adjusting for size differences between ellipsoids
# Example parameters for WGS84 → Arc 1960 # These are REGIONAL approximations — use official values for precise work. dx = 0 # X-axis shift (meters) dy = 0 # Y-axis shift (meters) dz = 0 # Z-axis shift (meters) rx = 0 # X-axis rotation (arcseconds) ry = 0 # Y-axis rotation (arcseconds) rz = 0 # Z-axis rotation (arcseconds) s = 0 # Scale factor (ppm) # 💡 For WGS84 → Arc 1960, enter the 7 parameters # provided by your national surveying authority for # the most accurate results.
⚠️ Important: 7-parameter values are region-dependent. Using parameters from a different region than your coordinate data will result in increased positional errors. Always obtain official parameters from your local surveying authority (e.g., NGII for Korea, Geoscience Australia, Ordnance Survey for UK, etc.).
WGS84 to Arc 1960 Conversion Guide
// WGS84 → Arc 1960 (7-parameter Helmert transformation)
// Between WGS84 ellipsoid and Clarke 1880 ellipsoid
// Step 1: Convert from WGS84 to geocentric Cartesian
// Using source ellipsoid: a = 6378137.0, 1/f = 298.257223563
N = a_source / √(1 - e²_source × sin²(φ))
X = (N + h) × cos(φ) × cos(λ)
Y = (N + h) × cos(φ) × sin(λ)
Z = (N × (1 - e²_source) + h) × sin(φ)
// Step 2: Helmert 7-parameter transform (WGS84 → Arc 1960)
// Parameters: dx, dy, dz (m), rx, ry, rz (rad), s (ppm)
//
X' = ΔX + (1 + s)(X + Rz·Y - Ry·Z)
Y' = ΔY + (1 + s)(-Rz·X + Y + Rx·Z)
Z' = ΔZ + (1 + s)(Ry·X - Rx·Y + Z)
// Step 3: Convert back to geodetic using Clarke 1880 ellipsoid
// a = 6378249.145, 1/f = 293.465
p = √(X'² + Y'²)
θ = atan2(Z' × a_target, p × (1 - f_target))
φ' = atan2(Z' + e²_target × (1 - f_target) × a_target × sin³(θ),
p - e²_target × a_target × cos³(θ))
λ' = atan2(Y', X')WGS84 to Arc 1960 requires a full 7-parameter Helmert transformation because the two systems use different ellipsoids and different datum origins. The conversion accuracy depends on the quality of regional 7-parameter values used.
- Enter your WGS84 coordinates in the input field (latitude, longitude, one pair per line)
- Enter the appropriate 7-parameter Helmert values (dx, dy, dz, rx, ry, rz, s) for your region
- Click the Convert button to transform coordinates from WGS84 to Arc 1960
- Review the converted Arc 1960 coordinates in the output field
- Copy the results or save them as an XLSX file for further use
- Ensure coordinates are within valid ranges before conversion
- 7-parameter values are region-specific; obtain them from local surveying authorities
- Verify a sample of converted coordinates on your target platform
- All conversions are performed client-side for complete data privacy