How to Square Numbers Near 1000 in Your Head

Updated 4 October 2026

Square numbers near 1000 by anchoring on 1000.

$996^2$996² = 992016

How do you square a number near 1000?

To square a number near 1000, take its distance from 1000 off the number, then attach the square of that distance as three digits. For 996², the distance is 4, so 996 − 4 = 992 and 4² = 16, written as 016, giving 996² = 992016. It works because (1000 − d)² is 1000 × (1000 − 2d) + d², so the first part counts thousands and the square of the distance fills the last three places. A number just above 1000 takes the distance added instead: 1007 is 7 above, so 1007 + 7 = 1014 and 7² = 49, written as 049, giving 1014049. From a distance of 32 onward, the square has four digits and carries into the thousands: 965 is 35 below 1000, so 965 − 35 = 930 and 35² = 1225, giving 965² = 930000 + 1225 = 931225. Check the last three digits first, because they always match the last three digits of the distance squared.

1. 996 sits 4 below 1000, so $996^2$996² is ${\left(1000-4\right)}^2$(1000 − 4)².

2. The distance comes off twice: 1000 − 2 × 4 is 992, or just 996 − 4.

3. Then attach $4^2$4², padded to three digits because the anchor has three zeros.

All 36 shortcuts: the Magic Tricks library.