Cartesian to polar CSV converter
Paste a CSV of `x,y` points and get `r,θ` back for every row — degrees or radians, signed or 0–360, with your `id` and `label` columns carried through.
About this tool
Polar coordinates describe a point by how far it is from the origin (r) and which way it lies (θ), instead of by how far along each axis it sits. The conversion itself is two lines of maths — r = √(x² + y²) and θ = atan2(y, x) — but doing it by hand for a few hundred survey points, antenna bearings, or scatter-plot samples is tedious and easy to get wrong in the second and third quadrants.
This converter runs the maths over a whole CSV at once, locally in your browser. It reads your header row, finds the coordinate columns (by name, by 1-based number, or by auto-detecting the usual spellings such as x/y, easting/northing, r/rho, theta/phi), converts every data row, and carries the columns it did not touch straight through to the output. Set the direction to Polar → Cartesian to go back the other way with x = r·cos θ and y = r·sin θ.
Worked example. Paste this:
id,x,y
p1,3,4
p2,-3,-4
p3,-1,0
with the angle unit set to degrees, the range set to signed, and 2 decimal places. The result is:
id,r,theta
p1,5.00,53.13
p2,5.00,-126.87
p3,1.00,180.00
p1 and p2 are the same distance from the origin but sit in opposite quadrants, and the angles differ by 180° — that is atan2 doing its job. Switch the range to positive and p2's angle becomes 233.13 instead.
Angle units and ranges. Degrees (a full turn is 360), radians (2π), gradians (400) and turns (1) are all available, and the same setting is used to read the angle when you convert polar → Cartesian. The signed range is atan2's natural (−180°, 180°]; the positive range wraps negative angles up into [0°, 360°). Both scale with whichever unit you pick.
Limits and edge cases. Input is capped at 5 MB and 200,000 data rows. Numbers are 64-bit floats, so about 15–17 significant digits are meaningful and the decimal-places control tops out at 15. The origin (0, 0) returns r = 0 and θ = 0, since no direction is defined there. A cell that is empty or is not a number stops the run and names the offending row and column rather than quietly emitting a blank. Delimiters are sniffed from the first non-empty line (comma, semicolon, tab or pipe) and CSV output is written back with the same one. This tool is planar only — it does not do 3D, cylindrical, spherical, or geodetic (lat/lon) coordinate systems, and it does not draw plots.
FAQ
Why is my angle negative?
The default range is the signed one, (−180°, 180°], which is what atan2 returns and what most maths libraries use. Points below the x-axis therefore get a negative angle: (3, −4) is −53.13°. If you would rather see compass-style values from 0 up to a full turn, set the angle range to positive and that same point becomes 306.87°.
Does it handle all four quadrants correctly?
Yes. The conversion uses atan2(y, x), not arctan(y / x). Plain arctan only produces angles between −90° and 90°, so it collapses (3, 4) and (−3, −4) onto the same answer and blows up when x is 0. atan2 looks at the signs of both coordinates, so (3, 4) gives 53.13°, (−3, −4) gives −126.87°, and (0, 5) gives exactly 90°.
My CSV has id and label columns — will they survive?
Yes, as long as Keep other columns stays on. Every column that is not one of the two coordinate columns is copied through in its original order, and the two converted values are appended after them. So id,x,y becomes id,r,theta. Turn the option off if you want just the converted pair and nothing else.
How do I tell it which columns to use?
Leave both column fields empty and it auto-detects common header names — x, y, easting, northing for Cartesian input, and r, rho, radius, theta, phi, angle for polar input. If your headers are unusual, type the exact header name (matching is case-insensitive) or a 1-based column number, such as 2 and 3. With First row is a header turned off, the columns are named column1, column2, … and the first two are used by default.
Can it convert polar coordinates back to x and y?
Yes — set the direction to Polar (r, θ) → Cartesian (x, y). It reads the radius and angle columns, interprets the angle in whichever unit you selected, and emits x = r·cos θ and y = r·sin θ. Round-tripping (3, 4) through polar and back returns 3 and 4 again, subject to the decimal places you asked for.
Is my data uploaded anywhere?
No. The conversion is a small WebAssembly module that runs entirely in your browser tab. The CSV you paste is never sent to a server, and the same code is what the command-line version runs locally.
Developer & Automation Access
Run it from the terminal
Same engine as this page, headless — via the gizza CLI:
gizza tool cartesian-to-polar-csv "x,y
3,4
-1,1
0,-2.5"New to the CLI? Get gizza →
Open it by URL
Pre-fill and auto-run this tool with query parameters — the names match the API/CLI:
https://gizza.ai/tools/cartesian-to-polar-csv/?csv=x%2Cy%0A3%2C4%0A-1%2C1%0A0%2C-2.5&direction=cartesian_to_polar&x_column=auto%20%E2%80%94%20e.g.%20x%2C%20easting%20or%202&y_column=auto%20%E2%80%94%20e.g.%20y%2C%20northing%20or%203&angle_unit=degrees&angle_range=signed&decimals=6&delimiter=auto&has_header=true&keep_columns=true&output=csvMachine-readable descriptor: tool.json — title + parameters JSON Schema for agents.