Racira CAD

Coordinate Input Tool

Input

The classic check: (30, 40) must give r = 50 and θ = 53.13°; entering r = 50 with θ = 53.13° must return (30, 40).

Result

Radius r50.000 mm
Angle θ (0–360°)53.130°
Angle θ (−180…180°)53.130°
QuadrantI

What is Coordinate Input Tool

Coordinate Input Tool converts between the two coordinate systems a CAD user meets daily: Cartesian (X and Y) and polar (radius and angle). In Cartesian mode you enter X and Y and it returns the radius — the square root of X squared plus Y squared — and the angle from the positive X axis computed with the two-argument arctangent, normalised to a full 0 to 360 degree circle, plus the equivalent signed angle in the minus 180 to 180 range and the quadrant.
In polar mode the conversion runs the other way: X is the radius times the cosine of the angle and Y is the radius times the sine, with the angle interpreted in degrees. The unit selector covers millimetres, centimetres, metres, inches and feet and labels the linear outputs — the radius in Cartesian mode and X and Y in polar mode — while angles are always in degrees.

How to Use Coordinate Input Tool

  1. Step 1: Choose the Conversion direction — Cartesian to Polar, or Polar to Cartesian. The input fields switch to match.
  2. Step 2: In Cartesian mode enter X and Y; in polar mode enter the radius and the angle in degrees. The angle can be negative or above 360 — it is normalised automatically.
  3. Step 3: Pick the Unit so the linear result is labelled correctly. Angles are always degrees.
  4. Step 4: Read the Result panel: in Cartesian mode the radius, the 0–360 angle, the signed −180 to 180 angle and the quadrant; in polar mode the X and Y values.
  5. Step 5: Check the classic case: (30, 40) must return r = 50 and θ = 53.13 degrees, and entering r = 50 with θ = 53.13 must return (30, 40).
The quadrant row is the fastest sanity check: a point in the third quadrant — both coordinates negative — must report an angle between 180 and 270 degrees, so if your answer comes out near 53 degrees for (−30, −40) something is wrong with the input order. The signed angle output covers users whose workflow expects bearings expressed in the minus 180 to plus 180 convention.

Why Use Coordinate Input Tool

CAD tools mix the two systems constantly: hole tables and point arrays are Cartesian, while rotation, polar array spacing, and features placed by radius and angle are polar. Converting by hand means remembering which quadrant flips the sign of the sine and cosine, which is exactly where 180-degree errors are born — a point that should land at (−30, 40) lands at (30, 40) and the part is mirrored.
The tool also earns its keep reversing the other way: reading a radius-and-angle callout off a drawing and typing it into a Cartesian-based parametric model, or turning a measured X/Y deviation into the radius that a dial indicator or a true-position check expects. Because it runs in the browser with no upload, you can convert dimensions for proprietary parts without sending geometry anywhere.

Privacy & Security

This tool runs entirely in your browser — no data ever leaves your device. There is no server round-trip, no upload, no logging, and no account required. Your input is processed locally using client-side JavaScript and is never stored, transmitted, or accessible to anyone else. When you close the tab, everything disappears.

Frequently Asked Questions

Why does (−30, −40) give 233.13 degrees and not 53.13?

Because the point is in the third quadrant, where both coordinates are negative. The two-argument arctangent places the angle by the signs of both inputs: 53.13 degrees describes the first quadrant, and the third-quadrant point is exactly 180 degrees around the circle, at 233.13 degrees. This is the quadrant mistake the signed-angle output exists to catch.

What is the difference between the 0–360 and the −180 to 180 angle?

They are the same direction written two ways. An angle of 300 degrees equals minus 60 degrees — both point to the same ray. Some CAD commands and inspection reports expect the wrapped form and others the signed form, so the tool shows both rather than making you convert mentally. Choose the row that matches what your downstream consumer accepts.

Can the tool convert an angle given in radians?

Not directly — the angle fields are in degrees. To convert, multiply the radian value by 180 divided by pi before entering it: 1 radian is about 57.2958 degrees, so a common quarter-turn of pi over 2 radians becomes 90 degrees. The tool then treats the result like any other degree input.

What happens if I enter a negative radius in polar mode?

The conversion still runs, and the math works: a negative radius points in the opposite direction, which is the same as adding 180 degrees to a positive radius of the same magnitude. If you did not intend that, flip the sign of the angle instead — the tool accepts either, so check the X and Y signs in the result before using them.