Measuring a room without lying to yourself
Run a tape measure along the two walls at floor level, not across furniture, and write the numbers down in one unit. A room that measures 12 ft 6 in is 12.5 ft: divide the inches by 12 before multiplying, because 12 ft 6 in × 10 ft is 125 sq ft, not 126. Mixed-unit slips like that are the single most common way people end up a box short of flooring.
Measure each room separately rather than pacing off the whole floor plan. Walls, closets and hallways make "the whole upstairs" much harder to estimate in one go than three rooms added together.
The formulas, shape by shape
Rectangle or square: length × width. This covers most rooms, decks, and lawns.
L-shape: draw one line splitting the L into two rectangles, calculate each, and add them. A 20 × 12 living room with an 8 × 6 nook is 240 + 48 = 288 sq ft. Any straight-walled floor plan, however lumpy, breaks into rectangles the same way.
Circle: π × radius², and the radius is half the diameter. A 10 ft diameter patio is π × 5² ≈ 78.5 sq ft.
Triangle: base × height ÷ 2, where height is the straight-line distance from the base to the opposite corner, not the length of the slanted side.
Converting between units
The foot is defined as exactly 0.3048 meters, which makes one square meter 10.7639 sq ft and one square foot 0.0929 m². A square yard is exactly 9 sq ft, and an acre is exactly 43,560 sq ft: a 100 ft × 100 ft lot is 10,000 sq ft, just under a quarter acre.
Carpet in the US is often priced per square yard while tile and laminate are priced per square foot. Divide sq ft by 9 for sq yd before comparing quotes, or a $30/yd² carpet will look nine times pricier than a $3.30/ft² one that costs the same.
From area to a shopping list
Flooring is not bought at exactly the room area. Cuts, breakage, and pattern matching waste material, so the working rule is to order 5-10% extra, closer to 10% for tile laid diagonally or planks in a small room with many doorways. For a 288 sq ft floor, that means ordering 300–320 sq ft and keeping the leftovers for repairs.
Paint works from wall area instead: perimeter × wall height, minus windows and doors. A gallon of interior paint covers roughly 350–400 sq ft per coat, per the coverage figure printed on the can.