Field guide
A checked local coordinate transformation
A reproducible result records what the parameters mean, where they came from and the order in which they act.
Start with supplied local parameters
Use this tool to rotate, translate and optionally scale a set of planar coordinates when the transformation parameters are already known. Typical tasks include moving a design layout into an agreed local frame, applying a documented orientation change, or shifting a temporary construction grid. The page keeps a correspondence between every original record and its result so you can review the operation before preparing a new point file. It does not estimate parameters from control pairs or determine which coordinate reference system your file uses.
Write down the source of the parameters and the purpose of the change. An angle copied from a drawing, an approved grid adjustment and a transformation derived from surveyed control have different meanings. A successful calculation only shows that the specified arithmetic can be performed; it does not establish that those parameters are appropriate for the project. Retain an independent check point that was not used to choose the parameters, and compare its expected result before accepting a field deliverable.
Map the input coordinates deliberately
Read a CSV or TXT point file, inspect the column preview and confirm the header, easting, northing and optional height fields. Point identifiers, descriptions and extra columns remain associated with their original rows. Leading zeroes in point names are preserved in the point CSV. If an input record has a blocking error, resolve it before applying a transformation; the tool does not quietly drop the difficult rows and export the rest as a complete job. XLSX workbooks are also accepted for this input: explicitly choose the worksheet, and replace formulas, dates or error cells with plain values before importing.
All horizontal coordinates, the center and east and north translations must use one consistent planar unit. The source unit selectors label the supplied values rather than converting them. Elevation can have its own declared unit, and the separate elevation offset must use that unit. Do not use longitude and latitude as if they were eastings and northings. Their angular values require a suitable geodetic operation or projection before a local planar rotation is meaningful.
Choose the center and point rotation direction
The rotation center C is an explicit easting and northing. With no translation, a point at C stays at C under both rotation and uniform scaling. Rotating around the coordinate origin is therefore different from rotating around a site control point, even when the angle is the same. Inspect the center coordinates with the same care as the angle. A misplaced decimal or swapped axis can produce a plausible-looking shape in a completely wrong location.
Direction describes the motion of points on a north-up, east-right plane. Counterclockwise 90 degrees moves an eastward vector to the north; clockwise 90 degrees moves it south. This is not a surveying azimuth measured clockwise from north, and it is not the same convention as rotating the coordinate axes. Enter decimal degrees from 0 through 360, with at most twelve fractional digits. Convert compact degree-minute-second values first rather than interpreting a value such as 90.3015 as ninety degrees, thirty minutes and fifteen seconds.
Read the execution order as part of the parameters
The default order rotates and scales about C, then applies the translation T. In vector form, the result is P′ = C + k R(P − C) + T. R is the selected point rotation and k is the positive uniform planar scale. Translation values are signed coordinate increments: a positive east shift moves the final position east and a negative north shift moves it south. Rotation and uniform scale share the same center and can be combined in this order.
The alternative translates first and then rotates and scales about the same fixed center: P′ = C + k R(P + T − C). Here the translation vector is itself affected by the later rotation and scale. For C = (0, 0), P = (1, 0), a counterclockwise 90 degree rotation and T = (10, 0), the default order gives (10, 1), while translating first gives (0, 11). This difference is why a report needs the execution order as well as the numerical values. The center remains fixed in the original coordinate frame in both modes.
Keep planar scale separate from height
Uniform scale is optional and defaults to a factor of one. Enable it only when the intended positive factor is known. A factor of 1.25 multiplies horizontal separations between points transformed together by 1.25; a factor of 0.5 halves them. Zero and negative factors are rejected because this workflow is for a nondegenerate orientation-preserving local similarity operation, not flattening or reflecting a layout. The factor is dimensionless and is not a substitute for an unexplained change of coordinate units.
Planar scaling never scales elevations. Height handling is an independent additive operation, Z′ = Z + dZ, enabled separately. A nonzero height offset requires a known height for every selected record. Unknown heights remain unknown when the offset is disabled or zero; they are never filled with a fabricated zero. The tool does not apply geoid corrections, vertical datum models, tilts or a three-dimensional rotation. If those are required, use a workflow that explicitly represents those operations and their supporting reference data.
Apply to all points or an explicit subset
Choose all source records when the entire set belongs to the same operation. For a subset, enter unique physical source record start lines separated by commas or spaces. The line numbers refer to the file locations, not to point names. A file with a header normally starts its first point on line two, and a quoted multiline record uses its starting line. The before-and-after table includes the source line and identifier so the selection can be checked without guessing.
Unselected records remain unchanged in the exported point table, in their original order and with their original fields. Distances are preserved by rotation and translation only for pairs that undergo the same operation. A changed point and an unchanged control point may move closer together or farther apart. When a subset is intentional, record why it was selected and check the boundary between changed and unchanged records. A preserved row count alone does not prove that the correct points were chosen.
Review coordinate differences before applying
The result summary lists the center, angle, direction, translations, effective planar scale, height offset, execution order and unit labels. The table shows original coordinates, new coordinates and signed differences for every record. Select a row to inspect the full coordinate strings, or select a point pair in the north-up preview. Blue represents the source and orange the result. The diagram is a bounded overview without a basemap, while the complete table and downloads retain every record.
Review at least a known point, a distant point and any record outside the selected scope. Check that the shape has the expected orientation and that the translation is applied at the intended stage. Then choose Apply reviewed transformation to enable the point CSV. Editing parameters invalidates the old preview and disables its point download, requiring a new calculation and review. This helps prevent a file generated with yesterday's center or an earlier order setting from being mistaken for the current result.
Save a result that can be checked again
The point CSV retains the source column order, point names, descriptions and extra fields, adding a header if the input did not contain one. Only the selected coordinate fields change. The before-and-after audit CSV records all rows and their selection state. Spreadsheet-safe text in the audit may include a protective apostrophe; use the point CSV for raw point interchange. The JSON report includes source values and mapping, parameters, sine and cosine values, the effective scale, the formula, time and applied state.
Input is limited to 100,000 records and 10 MiB, and the point CSV must also fit within 10 MiB. Processing runs locally in a worker; cancelling retains the inputs. Cardinal rotations use exact sine and cosine values, while other angles use finite trigonometric precision. Decimal arithmetic helps retain small changes at large coordinate origins, but it cannot turn approximate input parameters into survey accuracy. Displayed differences are rounded to six decimals, with scientific notation for very small nonzero values. Exports retain the calculated values for independent verification.
Understand the boundary with reference-system conversion
A known local rotation, translation and uniform scale may form one step in a documented coordinate workflow. It does not by itself identify State Plane zones, convert between national datums, apply time-dependent crustal motion, or account for projection distortion across a large area. If the source and destination are named coordinate reference systems, use an appropriate CRS transformation with the required area of use, units and reference data. Do not infer those choices from a filename or from the visual appearance of the preview.
For a final numerical check, compare a pair of original points with the same pair after transformation. With scale one, their horizontal separation should agree within numerical precision; with a positive factor k, the new separation should be k times the original. Check heights separately against the chosen additive offset. Reopen the exported point file in the receiving software and verify at least one record to confirm its column interpretation, then archive the original file and parameter report alongside the result.