Three distances, one line
Stretch something between two monuments and you can get three different numbers depending on what you mean. The slope distance is what the instrument actually measured, along the line of sight. The horizontal distance is that reduced for the vertical angle, and it is what appears on a plan as a dimension. The grid distance is the horizontal distance reduced to the ellipsoid and then scaled onto the map projection, and it is what you get if you compute the length between two published state plane coordinates.
On a short flat line in the middle of a zone all three are nearly the same and nobody has to think about it. On a long line, on a hill, near the edge of a zone, they are not, and the difference lands in the third or fourth significant place — small enough to look like a mistake, large enough to matter.
The elevation factor
Your line sits above the ellipsoid by however high the ground is, adjusted by the geoid separation. Both the line and its projection onto the ellipsoid subtend the same angle at the centre of the earth, and arc length goes as radius, so the projection is shorter in the ratio R over R plus h. That is the elevation factor and it is always less than one for anything above the ellipsoid.
The size of it is easy to carry around: about one part per million for every twenty-one feet of height. The default site is 1,450 feet of elevation with a geoid separation of minus 92.5, so it sits 1,357.5 feet above the ellipsoid and the elevation factor is 0.99993507 — 65 parts per million, or 0.34 feet on a mile. A site at sea level loses almost nothing. A site a mile up loses about 250 ppm, which is 1.3 feet on every mile you measure.
Note that it uses the ellipsoid height, not the elevation. In the lower 48 the geoid sits below the ellipsoid, so the separation is negative and typically somewhere in the tens of metres, which means the ellipsoid height is meaningfully smaller than the elevation. The value is entirely local and comes from a geoid model, not from a rule of thumb.
The grid scale factor
A map projection cannot lay a curved surface flat without distorting it, and every projection makes a choice about where the distortion goes. On the usual state plane zones the scale is slightly too small along the middle of the zone and slightly too large at the edges, with two lines in between where it is exact. The grid scale factor is how much the projection has stretched or shrunk your particular line, and it depends on where you are.
It comes from the projection: from your published control sheet, from geodetic software, or from the metadata that came with the job coordinates. There is no way to guess it and no single value, which is why this page takes it as an input and gives it no default worth trusting.
The combined factor, and the fifth decimal place
Multiply the two and you have the combined factor. It usually sits between about 0.9997 and 1.0001, and the interesting digits are the fifth and sixth. Saying it in parts per million helps: a combined factor of 0.99993 is minus 70 ppm, which is 0.07 feet per thousand feet and about 0.37 feet per mile.
Whether that matters depends entirely on the work. Setting a fence line across a suburban lot, it does not. Staking a mile of pipeline off state plane coordinates, an unapplied combined factor puts the far end a third of a foot out, and it does so systematically rather than randomly, so no amount of care in the field recovers it.
Area applies it twice
This one catches people who are otherwise careful. Area has units of length squared, so it scales as the square of the combined factor. A factor of 0.99993 costs 70 ppm on a distance and about 140 ppm on an area. On a hundred acres that is about 0.014 acres, which sounds negligible until it appears in the third decimal place of an acreage on a plan that also lists a deed call to two.
The practical consequence is that an acreage computed from grid coordinates and an acreage computed from ground distances are not the same number, and neither is wrong. Which one belongs on the plan is a question about what the plan is for, and it should be stated on the face of the drawing rather than left for a reader to work out.
Ground jobs and grid jobs
Two common conventions. Some projects publish a single combined factor for the whole site and work in ground distances throughout, so that a dimension on the drawing is a dimension you can tape. Others work entirely on grid, and every staking dimension has to be converted. Both are defensible. What is not defensible is a set of drawings that does not say which one it is on, and the resulting arguments about a few tenths are one of the more predictable ways a project loses a week.
Questions people ask
What is the combined factor?
The elevation factor multiplied by the grid scale factor. The first reduces a distance measured at your elevation down to the ellipsoid, and the second scales it from the ellipsoid onto the map projection. Multiply a horizontal ground distance by the combined factor to get a grid distance, and divide to go the other way. It usually sits within a few hundred parts per million of one, which is a few tenths of a foot per mile.
How do I find the grid scale factor for my site?
From your published control sheet, from the geodetic software that produced the coordinates, or from the metadata that came with the job. It is a property of a specific projection at a specific position and there is no general value, so this page takes it as an input rather than computing one. Anything that offers you a scale factor without knowing which projection you are on is guessing.
Why do I need the geoid separation?
The elevation factor uses the height above the ellipsoid, not the elevation above sea level. Those differ by the geoid separation, which in the lower 48 is commonly negative and in the tens of metres. Using the elevation directly instead of the ellipsoid height puts the elevation factor out by roughly the separation over the radius, which can be several parts per million and is a systematic error rather than a random one.
How much does the combined factor actually matter?
It is roughly one part per million for every twenty-one feet of elevation, plus whatever the projection is doing. On the values in the form — 1,450 feet of elevation, a geoid separation of minus 92.5, scale factors near 0.99994 — the combined factor is 0.99987657, which is minus 123 parts per million: 0.123 feet on a thousand and 0.65 on a mile. Irrelevant across a suburban lot, plainly visible over a mile of pipeline staked from grid coordinates, and systematic rather than random, so care in the field does not recover it.
Does the combined factor apply to areas?
Yes, and twice, because area has units of length squared. A factor of 0.99993 shortens a distance by 70 parts per million and an area by about 140. On a hundred acres that is roughly 0.014 acres. An acreage computed from grid coordinates and one computed from ground distances are genuinely different numbers, and the plan should say which it is quoting.
Should the project be on ground or on grid?
Both conventions are in use and both work. A ground job publishes one combined factor for the site and keeps every dimension tapeable. A grid job keeps everything in the projection and converts when staking. The failure mode is not choosing one, or choosing one and not saying so on the drawings. That is a decision for whoever is responsible for the survey, not something arithmetic settles.