Area of a Square Calculator

Calculator

Shareable link: current

Solve using Pick the known quantity

Length unit

Area unit

Precision

Value (side)

History

#	Method	Unit	Area unit	Value	Side	Perimeter	Diagonal	Area

Formula used

The area of a square depends on the input known:

A = s² from side length
A = d² / 2 from diagonal
A = (P / 4)² from perimeter
s = √A from area

Derived relations: d = s√2, P = 4s.

How to use this calculator

Select the method: side, diagonal, perimeter, or area.
Choose length and area units then set precision.
Enter the known value and click Calculate.
Review results, preview, and optionally add to history.
Export single run or full history as CSV or PDF.

Batch calculations

One item per line: method,value,unit,areaUnit(optional) e.g. side,12,cm or area,200,cm,m2

#	Method	Value	Unit	Area unit	Side	Perimeter	Diagonal	Area

Applications and Use‑cases

Estimating **tile** or **paver** coverage from room dimensions.
Calculating **paint**, **sealant**, or **coating** coverage needs.
Planning **garden beds**, **patios**, and **walkway** footprints.
Checking **engineering drawings** and **CNC cut plans** quickly.

Unit conversion cheatsheet

Length unit	Area unit (default)	1 m² equals	1 ft² equals
mm	mm²	1,000,000 mm²	92903.04 mm²
cm	cm²	10,000 cm²	929.0304 cm²
m	m²	1 m²	0.09290304 m²
in	in²	1550.0031 in²	144 in²
ft	ft²	10.76391 ft²	1 ft²

Common scenarios and outputs

Side (cm)	Perimeter (cm)	Diagonal (cm)	Area (cm²)
10	40	14.142	100
25	100	35.355	625
50	200	70.711	2500
120	480	169.706	14400

Quality checks and tolerances

Zero or negative inputs are invalid and blocked by validation.
Precision is clamped between 0 and 10 to avoid rounding drift.
Area from perimeter uses (P/4)²; confirm units first.
Diagonal tolerance derived from d = s√2 should match results.

Frequently Asked Questions

1) What inputs can I use?

You can enter side, diagonal, perimeter, or area. The calculator converts between these using exact relations. Choose units, set precision, and view all derived values instantly without extra steps.

2) Which unit should I pick?

Select the unit matching your measurement. Length units are mm, cm, m, inches, and feet. Area units can follow length automatically, or you can fix mm², cm², m², in², or ft² for consistent reporting.

3) Why is my area different?

Check the method and units. Perimeter must be a total length around the square. Diagonal relies on the √2 relation. Ensure precision isn’t truncating outputs. Recalculate after changing units or inputs.

4) How does batch mode work?

Enter one case per line: method,value,unit,areaUnit(optional). For example: side,12,cm or area,200,cm,cm2. Run batch, review results in the table, and export a CSV summary.

5) Can I save and share runs?

Yes. Click “Add to history” to store the current results locally. Use the share link to copy a URL with your settings and input, so others can open the calculator prefilled for review.

6) Are formulas exact or approximations?

The formulas are exact: A = s², d = s√2, and P = 4s. Diagonal uses √2, which displays rounded. Increase precision for tighter agreement across outputs and exported files.