If you're setting out a large square or rectangle (with batterboards) by yourself with no one to read the diagonal from the tape as you adjust the string line at the batterboard to get it square (get the diagonal right), after you get it 'close' (eyeball it), measure the diagonal and enter it here to calculate how far to move the string line at the batterboard, to square it.

The Red lines are what you have now
The Black lines are where you need to be
The distance to move the string line is marked above the batterboard at the top of the diagram. Make sure the Reference Length, Side length and Batterboard Gap are accurate first.

If your Reference Length is flush on an existing structure, and there's no batterboard behind it, you're good to go. If the layout is separate, and needs 4 corner batterboards, first find the 2 end Reference Length points (square off a boundary?) and drive stakes at each end of the Reference Length.

These 2 points will stay put, and must be in the correct position. (they're reference points). Next place the batterboard for the first side (as per diagram at top) and pull a line from the (permanent) reference point stake to the batterboard (eyeball it for square).

Mark the Side Length (permanent marker) on the line from the Reference Length stake to measure diagonal to. Use this calculator to adjust the line position to square the first side, then pull a line from this position on the batterboard BACK OVER THE REFERENCE POINT STAKE to position the line on the lower batterboard.

Now you have 1 side square from the Reference points, you can easily place the rest of the batterboards and square UP the sides (check the diagonals).