geoprimsField-grade geospatial math

State plane coordinates explained

The flat grids US surveyors work in, how to find the right zone, and the 2 ppm foot that moves coordinates by feet.

For surveyors · updated 2026-09-23

The State Plane Coordinate System of 1983 (SPCS 83) divides the United States into zones, each with its own flat grid on NAD 83. A position in a zone is an easting and a northing in meters or feet, like 1,347,294.025 ft E, 413,222.374 ft N in Pennsylvania South. The zones are small enough that grid distances stay close to ground distances, which is why surveyors, engineers, and county GIS offices use them.

Why it matters

Deeds, plats, road plans, and parcel maps in the US are often tied to state plane coordinates. A state plane grid is flat, so bearings and distances can be computed with plane trigonometry, the way a surveyor works in the field. UTM zones are 6° wide and can distort distance by as much as 1 part in 1,000 (see UTM coordinates). State plane zones are drawn to keep that much smaller.

How the zones are designed

The original state plane systems of the 1930s were designed to keep distortion under 1 part in 10,000, the accuracy of a steel tape at the time, according to NGS Manual NOS NGS 5. States that could not meet that with one zone got several. Most states kept the same zones for SPCS 83.

Each zone uses one of three conformal projections, chosen for the zone’s shape:

Projection Used for Examples
Lambert conformal conic Zones long east to west Colorado North, Central, and South; Pennsylvania North and South
Transverse Mercator Zones long north to south New York East, Central, and West; Florida East and West
Oblique Mercator A zone lying on a slant Alaska zone 1, the panhandle

A state can mix types. Florida North is Lambert, while Florida East and West are transverse Mercator. New York Long Island is Lambert, and the rest of New York is transverse Mercator. Montana, Nebraska, and South Carolina chose a single zone for SPCS 83, and NGS notes that there the scale correction can exceed 1 part in 10,000.

Finding your zone

In most states, zone boundaries follow county lines. Alaska’s do not. The zone lookup tool searches by name or by point. For downtown Pittsburgh it returns two zones whose area boxes cover the point: Pennsylvania South (3702) and West Virginia North (4701). The tool then tells you to confirm the zone by county. Allegheny County is in Pennsylvania South.

Each zone has a four-digit NGS code, like 3702, and an EPSG code for GIS software. Pennsylvania South is EPSG 32129.

A worked example

Pittsburgh at 40.446111° N, 79.982222° W (NAD 83) in Pennsylvania South, zone 3702:

Result Value
Easting 1,347,294.025 US survey ft
Northing 413,222.374 US survey ft
Same point in meters 410,656.04 m E, 125,950.432 m N
Scale factor 0.9999595
Convergence −1.44825°

The scale factor means a grid distance here is about 40 parts per million shorter than the same distance on the ellipsoid, or about 0.04 ft in 1,000 ft. The convergence is the angle between grid north and true north at the point.

Compare UTM at the same spot. The UTM forward tool puts Pittsburgh in zone 17N with a scale factor of 0.999691696, about 308 parts per million short, or 0.31 ft in 1,000 ft. Here the state plane grid distorts distance almost eight times less, which is the point of the smaller zones.

US survey foot vs. international foot

The US has had two feet:

Unit Definition Status
International foot 0.3048 m exactly The US foot since 1959
US survey foot 1200/3937 m Deprecated by NIST and NOAA on December 31, 2022

They differ by 2 parts per million, about 0.01 ft in a mile. That sounds small, but state plane coordinates are big numbers. NIST notes that a coordinate of 1,000,000 ft changes by 2 ft if you swap feet. For the Pittsburgh point:

Unit Easting Northing
US survey feet 1,347,294.025 413,222.374
International feet 1,347,296.719 413,223.201
Difference 2.694 ft 0.827 ft

Reading the US survey foot numbers as international feet in the inverse tool plots the point 2.818 ft away, to the west-southwest.

NIST says NGS will keep providing SPCS 83 coordinates in US survey feet where a state defined them that way, as legacy data. The tools use each zone’s legal foot by default. Montana, for example, is in international feet, and Colorado and Pennsylvania are in US survey feet. NIST also says NGS’s new SPCS2022 uses the international foot only.

Common mistakes

Where the numbers come from

The zone definitions and projection equations are in NGS Manual NOS NGS 5. The foot definitions and the deprecation come from NIST and NGS. Start with the zone lookup tool, then convert with the state plane forward tool, which shows each step under “How we got this.”

Try it: Latitude and longitude to state plane (SPCS83)

The calculator below is the real tool, running its worked example. Change any value; nothing leaves your device.

1,347,294.025US survey ft

In Pennsylvania South (3702) the point is at easting 1,347,294.025 US survey ft, northing 413,222.374 US survey ft.

  • The US survey foot was deprecated by NIST and NOAA on January 1, 2023. Use it only for legacy data.
Northing
Zone
NGS zone code
EPSG code
Grid convergence
Point scale factor
Provenance
Computed by
geodesy.spcs.spcs83-forward 1.0.1, core 0.1.0
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
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.
Notes
1 shown with the answer
Cites
Stem, J. E., National Geodetic Survey, State Plane Coordinate System of 1983, NOAA Manual NOS NGS 5; International Association of Oil & Gas Producers (IOGP), Coordinate Conversions and Transformations including Formulas, IOGP Publication 373-7-2 (Guidance Note 7-2); Karney, C. F. F., Journal of Geodesy, Transverse Mercator with an accuracy of a few nanometers

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Sources

Every number on this page comes from the tools above, which cite their sources on their own pages under "How we got this." Found a mistake? Use "Report a problem" at the bottom of the page.