Latitude and longitude to state plane (SPCS83)

Model: SPCS83 zone definitions from the EPSG dataset on GRS 80: transverse Mercator (Krüger series), Lambert Conic Conformal (2SP), and Hotine Oblique Mercator (variant A) for Alaska zone 1

Show your work

1. Zone

   the state plane zone, each with its own projection and origin

   40.446111°, -79.982222° = Pennsylvania South (3702)

2. Scale factor

   how much the zone's projection stretches distance here

   at 40.446111°, -79.982222° = 0.9999595

3. Easting

   x from that projection, plus the zone's false easting

   -79.982222° east in Pennsylvania South = 1,347,294.025 US survey ft

The same steps an agent gets from the MCP server with explain: true.

Accuracy: Matches PROJ within 0.05 µm on 2,480 points across all 124 zones; inverse round trips within 1e-12°. The input must already be NAD83; this tool does not change datums.

When to use this: Use this for survey and engineering work in the United States, where plans, plats, and agency data are on State Plane coordinates: it converts NAD 83 latitude and longitude to easting and northing in any of the 124 zones, in meters, international feet, or US survey feet, with the convergence and scale factor the work needs.

Limitations: The input must already be NAD 83: passing WGS 84 or ITRF coordinates puts the result off by up to a meter or two, because this projects rather than transforms datums. Feet come in two lengths and the legal one differs by state, which the result states. A point outside its zone's extent still converts, with a warning, but the distortion grows.

Worked example: Pittsburgh in Pennsylvania South (US survey feet). Source: add-geodesy-suite scenario: 1,347,294.025 ftUS E, 413,222.374 ftUS N (±0.003 ftUS). It is golden test vector v026, and every build checks the tool still gives its answer within its tolerance.

Review: Not yet independently reviewed by a geodesist.

Last verified: 2026-09-18, when a maintainer last confirmed this tool's sources at the issuer. See the sources ledger.

Status: version 1.0.1, core 0.1.0. See this tool in the verification report.

Changes

• 2026-09-23, fixed: Identifiers no longer show digit grouping: the EPSG code in SPCS83 forward and zone lookup reads 32129, not 32,129, and the decimal year in magnetic declination reads 2026.71, not 2,026.71 (all version 1.0.1). SPCS83 forward in US survey feet also gave the deprecated-unit warning (LEGACY_UNIT) twice, once for easting and once for northing; every tool now gives it once per result. Values are unchanged. Changelog
• 2026-09-19, result change: State plane convergence and scale factor in the Hotine oblique Mercator zone (Alaska zone 1) are now computed with Richardson-extrapolated differences. They moved by up to 0.0000001°, well inside the published tolerance, and now agree between the forward and inverse tools. Changelog
• 2026-09-18, changed: The first six tools passed the stable verification bar: a derivation, an independent worked example, invariant and differential tests, and at least 20 golden vectors each. Changelog

Checked against: 26 golden test vectors (download the test vectors, each with its source and tolerance). See how results are checked and every source.

Sources

• State Plane Coordinate System of 1983, NOAA Manual NOS NGS 5, Stem, J. E., National Geodetic Survey, NOAA Manual NOS NGS 5 (reprinted with corrections). Zone constants (Appendix) and the Lambert and transverse Mercator mapping equations.
• Coordinate Conversions and Transformations including Formulas, IOGP Publication 373-7-2 (Guidance Note 7-2), International Association of Oil & Gas Producers (IOGP), Revised September 2019. Sections 3.2.1.1 (Lambert Conic Conformal 2SP, EPSG 9802) and 3.2.4 (Hotine Oblique Mercator variant A, EPSG 9812). Read free.
• Transverse Mercator with an accuracy of a few nanometers, Karney, C. F. F., Journal of Geodesy, Vol. 85, No. 8. pp. 475-485 (6th-order Krüger series).

Terms

EPSG: EPSG Geodetic Parameter Dataset

The IOGP registry of coordinate reference systems and transformations, each with a code such as EPSG:4326. Source: EPSG Geodetic Parameter Dataset

NGS: National Geodetic Survey

The NOAA office that defines the US National Spatial Reference System: datums, geoid models, and state plane coordinates. Source: State Plane Coordinate System of 1983 (NOAA Manual NOS NGS 5)

SPCS83: State Plane Coordinate System of 1983

124 zones of conformal projections on NAD 83, drawn so that distortion stays near 1 part in 10,000 within each zone. Source: State Plane Coordinate System of 1983 (NOAA Manual NOS NGS 5)