Corrego Alegre to WGS84 Converter
About Corrego Alegre Coordinate System
Corrego Alegre is a historic Brazilian geodetic datum used primarily before the adoption of SIRGAS2000. It uses the International 1924 (Hayford) ellipsoid (a=6378388m, 1/f=297) and requires 7-parameter Helmert transformation for accurate conversion to WGS84. Corrego Alegre remains important for working with legacy Brazilian mapping, cadastral records, and infrastructure data.
Corrego Alegre was established in the 1970s as the official geodetic datum for Brazil, replacing older local systems. It was named after the Corrego Alegre observatory in Minas Gerais. Before the adoption of SIRGAS2000 in 2005, Corrego Alegre was the standard reference system for all official Brazilian surveying and mapping projects.
Corrego Alegre is still widely encountered in legacy Brazilian maps, cadastral surveys, older infrastructure projects, and environmental studies. Converting Corrego Alegre data to modern systems (WGS84, SIRGAS2000) is essential for GIS integration and cross-border data sharing in South America.
Corrego Alegre served as the official geodetic datum for Brazil for over three decades, forming the basis for the country's national mapping and land surveying infrastructure.
Corrego Alegre to WGS84 conversion requires a 7-parameter Helmert transformation. Common approximate parameters are dx=-206, dy=172, dz=-6 (meters), but regional variations exist across different areas of Brazil.
Corrego Alegre uses the International 1924 (Hayford) ellipsoid (a=6378388m, 1/f=297), the same ellipsoid used by the European Datum 1950 (ED50).
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.
⚙️ 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.
Corrego Alegre uses a different ellipsoid and reference frame than WGS84. 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 Corrego Alegre → WGS84 # 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 Corrego Alegre → WGS84, 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.).
Corrego Alegre to WGS84 Conversion Guide
// Corrego Alegre → WGS84 (7-parameter Helmert transformation)
// Between WGS84 ellipsoid and Hayford 1909 (intl) ellipsoid
// Step 1: Convert from Hayford 1909 (intl) to geocentric Cartesian
// Using source ellipsoid: a = 6378388.0, 1/f = 297.0
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 (Corrego Alegre → WGS84)
// Parameters: dx, dy, dz (m), rx, ry, rz (rad), s (ppm)
// Reverse sign for inverse transformation
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 WGS84 ellipsoid
// a = 6378137.0, 1/f = 298.257223563
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')Corrego Alegre to WGS84 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 Corrego Alegre 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 Corrego Alegre to WGS84
- Review the converted WGS84 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