Four times bigger

Fifteen out of every sixteen pixels in a 4× result are computed rather than recorded. At that ratio the character of the method shows through the picture instead of hiding inside it: Lanczos leaves a visible bright edge along high-contrast boundaries, Mitchell reads as a soft focus that was not in the original, edge-guided keeps diagonals clean and does nothing at all for a field of grass.

None of those is wrong. They are different trades, and 4× is the factor where you have to actually make one. Open the loupe, hold compare, and switch methods while looking at the same three centimetres of the picture — it takes about twenty seconds and it is the only way to choose that is not guesswork.

Small text is first. Letterforms are defined by strokes one or two pixels wide, and there is no arithmetic that turns a two-pixel smudge back into a serif. Every method here will give you a larger, smoother smudge, which is the honest outcome — and it is worth knowing that a trained model would instead give you a crisp letter that may well be the wrong letter.

Small faces are second. A face thirty pixels across has no eyelashes, no pores and no lip edge to enlarge. At 4× you get a larger version of the same absence. If the picture is of a person and the person matters, the honest advice is to go back and find a bigger original rather than to spend an hour choosing a kernel.

• Double the sizeThe factor with the least to apologise for. Opens at 2× on a sharp source.
• Eight times overThe factor most likely to disappoint, offered anyway with the reasons attached.
• What enlarging can and cannot get backWorked through at 2×, 4× and 8×, with the part that is a guess named as one.
• Enlarged and still softSix reasons a bigger picture looks worse, and which one you actually have.