ISOMETRIC COORDINATES
Isometric Converter
Convert isometric tile coordinates to screen pixels and back using the standard 2:1 diamond projection.
2:1 DIAMOND PROJECTION
Convert tile and screen coordinates
Isometric coordinate guide
Every isometric game has the same two conversions: tile (x, y) to screen pixels for rendering, and screen pixels back to tile for mouse picking. This tool does both directions with the standard 2:1 diamond projection used by Civilization, classic RPGs, and most modern isometric games.
The 2:1 diamond projection
A 2:1 iso tile is twice as wide as it is tall (64×32, 128×64). The conversion: screenX = (tileX − tileY) × w/2, screenY = (tileX + tileY) × h/2. The minus sign is what creates the diamond stagger.
The inverse (for clicking): tileX = (screenX/w + screenY/h) / 2, tileY = (screenY/h − screenX/w) / 2. Floor both results to get the tile under the cursor.
Rendering order is half the battle
Isometric sprites need painter's algorithm sorting: draw tiles with larger (x + y) after smaller ones, and sort entities within a tile by y. That single rule fixes most z-fighting and overlap artifacts.
Tip: Keep your tile art at exactly 2:1 and round pixel positions to whole numbers — fractional offsets cause shimmering when the camera moves.
Frequently asked questions
How do I convert tile coordinates to screen?
screen = ((x − y)·tileW/2, (x + y)·tileH/2). This tool does it instantly for your tile size.
How do I know which tile the mouse is over?
Invert the projection: tile = ((sx/tileW + sy/tileH)/2, (sy/tileH − sx/tileW)/2), then floor. Use this tool to verify your math with real numbers.
What if my tiles are not 2:1?
The formulas still work — just substitute your real tile width and height. 2:1 is a convention, not a law.
Privacy note: isometric calculations happen in your browser. Nothing is uploaded.