Rectifying latitude calculator

What rectifying latitude means and how to supply geodetic latitude

This endpoint evaluates the classical e-one series: e squared equals f times two minus f; e-one equals one minus square root of one minus e squared, all over one plus that square root; then μ equals φ minus a coefficient times sin of two φ, plus terms in sin of four φ, six φ, and eight φ through order e-one to the fourth. Send the required field latitude as a JSON number or numeric string in decimal degrees; aliases lat, phi, and geodetic_latitude are accepted. Values outside that closed interval, missing fields, non-finite numbers, and non-numeric strings raise invalid_input with a message that names the field. Identical inputs always produce identical JSON because the path is pure series arithmetic with fixed WGS-84 constants—no wall clock, no random seed, and no external geodetic service.

Reading degrees, radians, meridian arc, and datum fields

On success the response echoes latitude, then reports rectifying_latitude_deg as μ in decimal degrees and rectifying_latitude_rad as the same angle in radians. geodetic_latitude_rad is the input converted by pi over one hundred eighty so callers can compare φ and μ in a single unit system without converting again. difference_deg is μ minus φ in degrees; on WGS-84 the magnitude is typically a few hundredths of a degree at mid-latitudes and vanishes at the equator and the poles where the series terms cancel or sin of multiples of pi over two become zero. meridian_arc_m is the north–south ground distance from the equator to the given latitude in metres, computed as rectifying_radius_m times μ in radians. rectifying_radius_m is R prime, the radius of the sphere of equal meridional perimeter, derived from the semi-major axis and powers of e squared. ellipsoid is always the string WGS-84; a_m is six million three hundred seventy-eight thousand one hundred thirty-seven metres; f is the flattening one over two hundred ninety-eight point two five seven two two three five six three; e2 and e1 are the first eccentricity squared and the rectifying series parameter, rounded for stable goldens. method is always snyder_e1_series. Prefer degrees when teaching or matching published tables; prefer radians and meridian_arc_m when wiring a projection pipeline; use difference_deg to sanity-check that μ and φ stay close on Earth-like ellipsoids. Validation failures are not charged under the prepaid API.

API usage, pricing, projection workflows, and practical limits

Send a JSON body with the required latitude field, then call the free in-browser rectifying latitude calculator for homework checks, lecture demos, and quick projection debugging without installing PROJ, GeographicLib, or a full GIS stack. Use the prepaid API when a mapping platform, curriculum generator, or coordinate-conversion pipeline needs a stable contract under KIT balance at $0.002 per successful item; validation failures never consume balance after the engine rejects the request. Pair this endpoint with degree-of-latitude length tools when you need local meridional scale, or with a full Transverse Mercator product when the next step is easting and northing rather than the auxiliary angle alone. This product does not convert to authalic, conformal, isometric, or geocentric latitude—those auxiliary angles serve area, angle preservation, or radius-of-curvature problems and are separate search intents. It also does not invert μ back to φ; inversion needs a different series or Newton iteration.