Create distinct side and result columns
Use A1 Length, B1 Width, C1 Area, D1 Perimeter and E1 Diagonal. Record one common length unit for both side inputs. With 15 in A2 and 8 in B2, the sheet describes a 15-by-8 rectangle. A diagonal is not an adjacent side; substituting it for width would change the problem. Keep source measurements and computed outputs visually separate so a copied result cannot accidentally overwrite an input used by other formulas.
Enter the forward formulas
Area in C2 is =A2*B2. Perimeter in D2 is =2*(A2+B2). Diagonal in E2 is =SQRT(A2^2+B2^2). The example returns 120 square units, 46 units and 17 units. Parentheses are essential in the perimeter formula: =2*A2+B2 counts only one width. Excel and Google Sheets support these arithmetic operations, but localized function names and argument separators may differ. Adapt the formula syntax without changing the geometric relationship.
Recover width from a known area
If A2 stores a positive known length and C2 stores known area, missing width is =C2/A2. For length 15 and area 120, width is 8. Do not simultaneously leave C2 as a formula dependent on that same width cell, or the sheet creates a circular reference. An inverse worksheet should distinguish supplied area from computed area. Use separate layouts or dedicated input cells rather than switching a formula cell into an input without documenting the change.
Recover width from perimeter or diagonal
Given length a and full perimeter P, width is P/2−a, valid only when P>2a. Given a and diagonal d, width is sqrt(d²−a²), valid only when d>a for a positive rectangle. For a=15, either P=46 or d=17 recovers width 8. Equal diagonal and side would collapse the other dimension to zero. An invalid square-root argument should remain an error to investigate rather than being replaced by zero through a broad error handler.
| Known values | Width relationship | Answer |
|---|---|---|
| Length 15; area 120 | 120/15 | 8 |
| Length 15; perimeter 46 | 46/2−15 | 8 |
| Length 15; diagonal 17 | √(17²−15²) | 8 |
Separate input cells avoid circular references. Positive-side feasibility checks are required.
Validate positive numeric measurements
A guarded area formula can use =IF(AND(ISNUMBER(A2),ISNUMBER(B2),A2>0,B2>0),A2*B2,NA()). Similar checks should protect inverse inputs and their feasibility conditions. Missing width is not a verified zero width, and text such as 8 m should not be mixed with the numeric field. Separate units from values before calculation. A plausible result is not evidence that imported numbers, decimal punctuation or spreadsheet references were interpreted as intended.
Keep unit conversions dimensionally correct
If the sides are 150 cm and 80 cm, area is 12,000 cm², perimeter is 460 cm and diagonal is 170 cm. Converting both side inputs to 1.5 m and 0.8 m gives area 1.2 m², perimeter 4.6 m and diagonal 1.7 m. The linear quantities divide by 100 while area divides by 10,000. A column format does not perform those conversions. Give each output its proper dimension instead of copying the same unit label across all result columns.
Audit formulas with scaling and inverse checks
Double both sides of the 15-by-8 example to 30 and 16. Perimeter and diagonal must double to 92 and 34, while area must quadruple to 480. Recovering width from the original area or diagonal should return 8. These checks test different equations and can expose a misreferenced cell. For very thin rectangles or nearly equal side and diagonal readings, rounding can obscure the smaller side; retain measurement precision and inspect whether the original data actually resolve it.
Compare with supported calculator modes
Use the Rectangle Calculator in two-side mode with 15 and 8, then verify one-side-plus-area or one-side-plus-diagonal modes with the same known values. Its inverse modes check constraints that a raw spreadsheet formula may leave unguarded. The tool does not execute pasted workbook expressions. Preserve the workbook's supplied-input labels, units, formulas and rounding policy. When both area and perimeter are supplied instead of a side, use the supported dedicated inverse mode rather than pretending area alone determines the two sides.
Preserve feasibility messages in inverse sheets
An inverse perimeter formula should reject a perimeter that is no greater than twice the known side. An inverse diagonal formula should reject a diagonal no greater than that side. These are mathematical conditions for a positive second dimension, not optional display preferences. A zero returned by a generic error handler could be mistaken for an acceptable narrow rectangle even though the original inputs were impossible.
If the source measurements are rounded, distinguish approximate reconstruction from exact equality. An area and perimeter may lie just outside a feasibility boundary because of rounding, but silently altering one measurement conceals that fact. Retain the supplied values, flag the conflict and obtain better information where necessary. A worksheet can show a scenario based on adjusted measurements only if the adjustment is explicitly identified.