Precision vs. Accuracy in Coordinates

A smartphone GPS app reads out 40.7484692, -73.9857064 — seven decimal places of latitude and longitude. The display invites the reader to trust the position to better than a centimetre. The actual fix, under open sky with a clear view of multiple satellites, is accurate to roughly 4.9 metres at the 95th percentile — about a half-million times worse than the displayed precision suggests. The trailing digits are real numbers, but they describe receiver arithmetic, not the position on Earth.

This article unpacks the precision-versus-accuracy distinction as it applies to coordinates. It cites the canonical NIST definitions, works through three real-world examples (consumer GPS, address geocoding, survey-grade observation), and lands on a single rule of thumb — five decimals — that prevents almost every false-precision bug in everyday coordinate work.

The NIST definitions

NIST's measurement-uncertainty guidance formalises the two terms:

• Precision describes the resolution or repeatability of a measurement. A repeated set of measurements that cluster tightly together is precise — regardless of whether the cluster is centred on the true value.
• Accuracy describes how close a measurement (or the mean of a set of measurements) is to the true value. An accurate measurement is centred on the truth — regardless of whether individual readings scatter.

The two properties are independent. The classic teaching device is a dartboard:

• High precision, low accuracy: a tight cluster of darts, all in the same wrong corner.
• High accuracy, low precision: darts spread widely but centred on the bullseye.
• High precision and high accuracy: a tight cluster on the bullseye.
• Low on both: a wide spread, miss-centred.

In measurement work, “precise but inaccurate” is the most common failure mode — a high-resolution instrument with a systematic bias produces readings that look authoritative but are reliably wrong. The opposite — accurate but imprecise — is rarer in practice because it requires repeated independent readings to detect.

In coordinates specifically

Coordinate precision is a property of the recording — how many decimal places of DD, how many digits of MGRS, how many arcseconds of DMS, how long a Plus Code is. The /learn/decimal-degrees-vs-dms article tabulates the ground-distance equivalents of each precision level; the short version is that one extra decimal of DD divides the uncertainty by ten.

Coordinate accuracy is a property of the source — what instrument produced the reading, under what conditions, against what reference datum. A coordinate from a smartphone GPS, from a geocoded street address, from a paper map, and from a survey-grade RTK observation all have different accuracy characteristics, and none of them are implied by the number of decimal places stored.

The two are independent in both directions:

• A high-precision recording with a low-accuracy source produces false precision: a number written to seven decimals when the underlying source is good to ~5 m.
• A low-precision recording with a high-accuracy source produces truncated information: a survey-grade observation rounded to two decimals loses the very precision that justified the survey.

Honest coordinate practice matches the recorded precision to the source accuracy. The matching is the whole discipline.

Three worked examples

A smartphone GPS reading: precise to mm, accurate to metres.

A modern smartphone in an open-sky environment fixes its position using GPS plus (depending on hardware) GLONASS, Galileo, and BeiDou. The receiver's internal arithmetic produces a position estimate with many digits of resolution — modern silicon outputs latitudes and longitudes with seven or more decimal places (sub-centimetre precision). Per GPS.gov, the actual horizontal accuracy is approximately 4.9 m at the 95th percentile under open sky. The leading five decimals (~1.1 m) match the accuracy budget; the trailing digits are arithmetic artefacts, not measurement signal.

An address-geocoded coordinate: precise to cm, accurate to metres.

A geocoder returns 40.748441, -73.985664 for the Empire State Building. The result has six decimal places (~11 cm precision). The underlying accuracy depends on the geocoder's data sources: typically 5 to 20 m for a rooftop geocoder in dense urban areas, 30 m or more for an interpolated street-segment estimate. The recorded precision overstates the source accuracy by about two orders of magnitude. The /tools/coordinates-to-address tool surfaces the confidence band alongside each candidate; relying on the decimal count alone is a recipe for the “why is the pin on the wrong building?” bug.

A surveyed monument: precise to mm, accurate to mm.

A geodetic control monument in the NOAA NGS database carries a coordinate established by repeated static GNSS observation, post-processed against the National Spatial Reference System and reported with full covariance. Horizontal accuracy: typically 1 to 2 cm. Recorded precision: seven or more decimals of DD. Here, the precision honestly reflects the accuracy. The recorded value carries the authority of the underlying observation.

In the first two cases, precision exceeds accuracy. In the third, they match. The first two are common; the third is what surveying work explicitly buys.

A fourth case worth naming: cellular and IP-based geolocation. Browser-derived locations that fall back from satellite GPS to cell- tower triangulation or to IP geolocation can be accurate to 50 to 500 m (cellular) or city-level (IP-derived) — but the API often returns six or seven decimals regardless, so the precision claims sub-metre resolution while the underlying accuracy is two to four orders of magnitude worse. The /tools/my-location result panel reports the browser-supplied accuracy estimate alongside the coordinate precisely to make this discrepancy visible to the reader.

The 5-decimal rule of thumb

A short heuristic that prevents most false-precision mistakes:

For coordinates derived from consumer GPS, store and display at most five decimal places of decimal degrees (about 1.1 m at the equator). Extra digits are decoration.

The rationale is direct. Civilian GPS, under open sky, produces ~5 m of accuracy; under SBAS / WAAS augmentation, ~1 to 2 m. Five decimals match the 1 m end of that range; a sixth decimal claims ~11 cm of meaningful resolution that the source does not have.

The 5-decimal rule does not apply when the source justifies more precision — survey-grade observations and post-processed static GNSS deserve seven decimals, sometimes eight. It does not apply when the source justifies less — IP geolocation returns city-level resolution where two decimals (~1.1 km) is already over-precise. The rule is calibrated to the most common coordinate source (consumer GPS) and is a default, not a ceiling.

A small historical footnote on why consumer GPS accuracy looks the way it does. From 1990 to May 2000 the US Department of Defense intentionally degraded civilian GPS accuracy through Selective Availability — typical civilian accuracy in that era was roughly 100 m at the 95th percentile. President Clinton ordered Selective Availability turned off on 2 May 2000; civilian accuracy improved by roughly an order of magnitude overnight. The 4.9 m headline figure from GPS.gov assumes the post-2000 unaugmented service; augmented services like WAAS / SBAS push accuracy further to 1 to 2 m routinely. The 5-decimal rule is calibrated to the contemporary service — applying it to a 1995-era logged coordinate would be a mismatch in the opposite direction.

The /methodology page documents Coordinately's internal application of the rule across tools and articles.

Format choice influences honesty

Some coordinate formats are self-limiting on precision and discourage false-precision bugs by construction:

• Plus Codes (Open Location Code) at length 10 (+CFRR) describe a ~14 × 14 m cell. Adding characters to length 11 takes the cell to ~2 × 2 m. The format quantises precision into named cells, so the reader knows the resolution by inspection.
• MGRS to one-metre precision (18TWL 8398 1075 style) is explicitly a 1 m cell. The digit count is the precision claim.
• UTM to whole metres similarly describes a 1 × 1 m cell.

In DD and DMS notation, by contrast, nothing on the page tells the reader where the precision floor is. A coordinate written to seven decimals looks identical whether it was measured by a survey monument or pulled from a smartphone — the format does not encode the source. This is one of the strongest arguments for ending coordinate strings with a source citation when accuracy matters; see How to Write Coordinates.

Reporting uncertainty honestly

The Coordinately tools surface accuracy band alongside numerical results wherever the underlying data carries one:

• /tools/elevation reports the dataset (USGS 3DEP for US points, OpenTopoData SRTM30m elsewhere) and the expected accuracy band for that dataset. USGS 3DEP elevations are typically accurate to better than 2 m vertical RMSE; SRTM30m is approximately 10 m vertical accuracy.
• /tools/distance-calculator reports the method used (Vincenty WGS84 by default, haversine fallback near antipodes) and the millimetre-level convergence target.
• The geocoding tools surface a per-candidate confidence band and full alternative-candidate list when the top result is not high confidence.

The pattern is to publish the accuracy claim alongside the precision, explicitly, rather than letting the digit count speak for the accuracy. A reader, an AI ingester, or a downstream tool can then weight the result correctly.

The site's public /accuracy page documents the standard.

Common misconceptions

“More decimal places means a more accurate coordinate.” False. Extra decimals are extra precision; accuracy is a property of the source, not of the recording. A 15-decimal latitude from a smartphone GPS is no more accurate than the same coordinate at five decimals — the trailing ten digits are arithmetic residue, not new information.

“Two precise readings that agree are accurate.” Not necessarily. Two readings from the same biased source agree precisely because they share the same bias. Agreement between independent sources is the test of accuracy; agreement between repeated readings from the same source tests only precision.

“Precision and accuracy are the same thing.” They are different properties of a measurement. NIST formalises the distinction; every metrological discipline preserves it. Conflating the two leads to false claims of accuracy supported only by trailing digits.

“Surveyed coordinates are always survey-grade.” Only when reported with the survey-grade datum, network, and uncertainty metadata. A historical survey monument with a recorded position from the 1930s may have lost accuracy through datum shifts (NAD27 → NAD83 → NAD83 epoch updates) even if the original observation was precise. The current NGS Coordinate Accuracy Standard documents the adjustment process; without it, a number from a survey database is a record, not a measurement.

“A geocoder's six-decimal output is rooftop-accurate.” Independent of the precision. Geocoders differ widely in their underlying data: some return rooftops, some return interpolated street segments, some return administrative centroids. The decimal count is implementation-defined; the source layer is the accuracy claim. Always read the confidence band, not the digit count.

“Sub-metre precision is always useful.” It is, when the source can support it. Survey-grade applications (boundary monumentation, infrastructure as-built records, geodetic control) genuinely need it. For navigation, delivery, and most consumer-facing coordinate work, sub-metre precision rounds to noise; centimetres of recorded precision are not useful in a context where the positioning error is ~5 m. Match precision to use case.