Fit, scale, dining and screen calculators

Four calculators: will a piece fit through a door and around a corner; how long a wall is on paper at your scale; how many seats a table gives and how much room it needs; and how far a screen sits for a given viewing angle.

Each calculator does geometry or arithmetic on the figures named under it. None of them knows your piece, your stair or your eyes: write each result on the sheet it belongs to and check it on the floor or with the seller.

Will it fit: a door and a hall corner

Measure the piece at its widest points (arms, feet, handles included) and each door fully open at its narrowest point, usually between the door stop and the open door's face. Enter the halls on each side of a corner as clear widths, wall to wall or rail to wall. The furniture you have explains each measurement.

Assumptions

• Doorway: the piece goes through on its two smallest sides, the smallest across the door's width and the next under its height. Joybird's fit guide (a retailer's method) says to measure the door fully open at its narrowest point and to allow 1 to 1.5 in for the delivery team's hands, and to add 3 to 6 in to the item's size for its packaging and the movers' hands together. The calculator marks a margin under 1 in "very tight" and under 1.5 in "tight". Convention
• Corner: the longest box of a given depth that can be carried level around a square corner is the smallest value, over the angle the piece makes with the hall, of a ÷ cos θ + b ÷ sin θ − depth ÷ (sin θ cos θ), where a and b are the two hall widths. With no depth it is the textbook ladder result, (a^2/3 + b^2/3)^3/2: for the 8 ft and 6 ft halls of exercise 323 in OpenStax's Calculus Volume 1, section 4.7, it gives 19.73 ft, which we checked against the formula; the derivation is set out on Anirdesh's ladder problem page. The version with depth is geometry derived from that textbook corner problem, not a formula quoted from a source. We checked it against the textbook answer with no depth, and by hand for two equal halls at 45 degrees, where it gives 2√2 × hall width − 2 × depth, the length of the piece's outer edge between the two outer walls. Physical principle
• The corner check tries the piece flat (its depth across the hall) and on its back (its height across the hall). A piece whose depth is not narrower than the narrower hall cannot be carried level around the corner at all; that result says so instead of giving a length.
• Not modeled: tipping a piece on end, legs or feet that come off, soft arms or cushions that compress, a stair's slope, rails and headroom, landings, a corner that is not square, and packaging. Article's measure-for-delivery guide (a retailer's method) covers the route checks this calculator leaves out. Test it

Scale and floor area

Turns a real length into its length on paper at the scale you draw at, and a length and width into floor area. Measure and draw the room explains drawing to scale.

Assumptions

• Drawn length = real length ÷ the scale's ratio (48 for 1/4 in to 1 ft, because 1 ft is 48 quarter inches). Area = length × width, for a rectangle; an L-shaped room is two rectangles added. Arithmetic only.
• The 1/4 in to 1 ft scale on graph paper with four squares to the inch, one square for 3 in of room, is the method in Virginia Cooperative Extension's Furniture Arrangement bulletin, an archived publication. Convention

Dining table seats and room

Counts seats from the table's edge and adds the clearance you choose behind the chairs on every side. Living and dining rooms explains the figures and when each applies.

Assumptions

• Seats: 24 in of table edge per diner, along each long side, and one at each end when the end is at least 24 in wide; a round table's seats are its circumference (π × diameter) ÷ 24. The 24 in figure and the clearance choices (32 in where no one passes, 36 in to edge past, 44 in to walk past, 60 in for a wheelchair to pass) are from the National Kitchen & Bath Association's Kitchen Planning Guidelines, as published in its free summary, which NKBA wrote for kitchen seating; we apply them to a dining table. Convention
• The 26 in alternative is from a Houzz practitioner article, which gives 26 in per person at round tables seating three to six and 24 in at six or more: How to Seat Your Dinner Guests in Comfort. Convention
• Room needed = table plus the chosen clearance on every side. "In your room" assumes the table is centered with its long side along the room's long side, and that nothing else stands in the clearance. A sideboard, a radiator or a door swing takes from it.

Screen viewing distance

Gives the distance at which a screen fills a 30 degree or a 40 degree share of your view, and the practitioner range. Enter your own seat's distance to see the angle it gives. Living and dining rooms explains each figure.

Assumptions

• Screen width = diagonal × 16 ÷ √(16² + 9²) for a 16:9 screen. Distance = (width ÷ 2) ÷ tan(angle ÷ 2). Geometry. Physical principle
• The 30 degree and 40 degree angles are as RTINGS reports them in its size-to-distance explainer: 30 degrees as SMPTE's minimum field of view, 40 degrees as its own recommendation for a cinematic setup. We did not read the SMPTE document, which is paywalled. Convention
• The 1.5 to 2.5 times the diagonal range is from Houzz's Key Measurements for Your Living Room, a practitioner article. The "distance ÷ 2 gives the diagonal" rule is from the AARP HomeFit Guide. Both are rules of thumb. Convention