Skip to main content
    GeoGiza
    Sign in
    Free tool

    Scale factor & convergence calculator

    The point scale factor k, grid convergence γ, elevation factor and combined factor for any projected system — with grid↔ground distance conversion for precise work.

    Scale factor calculator

    Point (WGS84) & elevation

    Enter the point by longitude/latitude (WGS84 from GPS); decimal or DMS accepted. Height is optional (metres above the ellipsoid) for the combined factor.

    Request technical support

    Need help with your survey project?

    Leave your email and our technical office will reach out for certified conversion and geodetic-adjustment support. The tool stays free, no sign-up.

    FAQ

    What does the scale factor k mean, and why is grid ≠ ground?
    The point scale factor k is the ratio of the grid distance (on the projection plane) to the distance on the ellipsoid at that point. When k > 1 the grid distance is longer than the ground; when k < 1 it is shorter. So a distance read off grid coordinates differs from the distance actually measured on the ground and must be corrected by the factor before precise work.
    Is grid convergence γ the same as magnetic declination?
    No. Grid convergence is the angle between true north and grid north; it comes from the projection alone and does not change over time. Magnetic declination is the angle between true north and magnetic north and varies with location and epoch. Confusing the two is a common orientation error.
    How is the combined factor computed with elevation, and which radius?
    The combined factor = scale factor k × elevation factor. The elevation factor = R / (R + h), where h is the point’s height above the ellipsoid. We use the Gaussian mean radius R = √(M·N) (the geometric mean of the meridional radius M and the prime-vertical radius N) at the point’s latitude, which is the appropriate radius for reducing distances.
    When do I apply the ground→grid correction on total-station work?
    A total station measures a horizontal ground distance. To place it on the projected grid, multiply the measured distance by the combined factor (ground→grid). To go the other way — to stake out a ground distance from grid coordinates — divide by the combined factor (grid→ground). Skip the correction only for low-precision work or near the line of zero distortion.
    Why do some belts show two different scales?
    Three belts in the registry are Cassini projections, which are non-conformal — their scale factor is direction-dependent, so the meridional and parallel scales differ. We show both honestly; use the scale in the direction of your line. Conformal systems (Transverse Mercator, UTM) have equal values, both equal to k.

    You may also need: Distance & bearing calculator · Arab-world coordinate converter · Traverse calculator (Bowditch) · Land area calculator · Distance calculator