2026-09-23 8 min read

Polygon Area Calculator

Free polygon area calculator — calculate polygon area with live unit conversion, waste allowance and cost estimates. Includes live results, step-by-step working, charts, material takeoff and cost estimates. No sign-up.

Calculator

Number of sides(count) Help

count

e.g. 6 for a hexagon

Side length(unit below) Help

unit below

Length of one equal side

Quantity(areas) Help

areas

Identical shapes

Waste allowance(%) Help

Extra for cuts and errors

Price (optional)($/sq ft) Help

$/sq ft

Leave blank for area only

Input unit

Takeoff plan

Item	Amount
Net areaCalculated, before waste	41.57 sq ft
Order quantityNet plus waste — buy this	45.73 sq ft
Square yardsOrder ÷ 9	4.62 sq yd
Square metersOrder ÷ 10.764	3.86 sq m
PerimeterAll sides added	24.00 ft

How to use this result

Primary result: 41.57 sq ft — verify it against a rough hand check before ordering.
Read the steps section to see every conversion and the exact formula path.
Use the breakdown table on the left as your order or bid checklist.
Re-run with worst-case dimensions so the plan covers the whole job.

Results

Normal

Total area

41.57sq ft

polygon area in square feet

Perimeter

24.00ft

Sum of all sides

Square yards

4.62sq yd

Divide square feet by 9

Square meters

3.86sq m

Divide square feet by 10.764

Order quantity

45.73sq ft

Net plus the waste allowance

Live results update as you type — currently showing 41.57 sq ft. Replace the defaults with your own measurements for an exact takeoff.

Visualizations

Area vs common rooms (sq ft)

41.6Your area

120Bedroom

400Garage

Net area vs waste allowance

Net area91%

Waste9%

Formula

The area of a regular polygon is n × s² ÷ (4 × tan(π ÷ n)), where n is the number of equal sides and s is the side length. Quantity multiplies the single-shape result; waste is applied last.

A = n × s² ÷ (4 × tan(π ÷ n))

Variables

Symbol	Name	Unit	Description
A	Area	sq ft	Total enclosed area.
n, s	Sides and side length	count, selected unit	Regular polygon: all sides and angles equal.
q, w	Quantity and waste	count, %	Identical shapes and the cutting allowance.

Explanation

Inputs convert to feet first, the shape formula runs at full precision, quantity multiplies the result, then waste is added. Conversions are exact division.

Step-by-Step Calculation

Follow each step to understand how the result is calculated from your inputs.

Step 1

Convert the side length to feet.

Side:4 → 4.00 ft

Sides:6

Result: s = 4.00 ft, n = 6

Step 2

Apply A = n × s² ÷ (4 × tan(π ÷ n)).

A = 6 × 4.00² ÷ (4 × tan(π ÷ 6))

Result: A = 41.57 sq ft

Final Answer

41.57

Worked Examples

See how the calculator works with different scenarios.

Scenario

The calculation run on the values above, showing the full path rather than only the answer.

Inputs

Result:41.57 sq ft

Calculation

1. Convert the side length to feet. → s = 4.00 ft, n = 6 2. Apply A = n × s² ÷ (4 × tan(π ÷ n)). → A = 41.57 sq ft

Result

41.57 sq ft

Interpretation

Order the net area plus a waste allowance (10% for flooring and paint-grade work, 15% for tile, 20% for diagonal layouts) and keep one spare box or 5% spare tile for repairs.

Understanding Your Result

Your Result: Total area: 41.57 sq ft

Typical range: Bathroom 40–60 sq ft · bedroom 100–180 sq ft · living room 200–400 sq ft · 2-car garage about 400 sq ft · 1 acre 43,560 sq ft.

What This Means

Your result is 41.57 sq ft — the net polygon area from your dimensions — what you measure on site, not what you order from the supplier

Why It Matters

Area drives every downstream number on a job: material quantities, cost estimates, bids and code checks. A small measuring error compounds across a whole floor, so modelling the area before buying is the cheapest form of due diligence.

Professional Interpretation

Order the net area plus a waste allowance (10% for flooring and paint-grade work, 15% for tile, 20% for diagonal layouts) and keep one spare box or 5% spare tile for repairs.

How this is calculated

The area of a regular polygon is n × s² ÷ (4 × tan(π ÷ n)), where n is the number of equal sides and s is the side length.

What drives the result

The dimensions in a single consistent unit, the quantity multiplier, the waste percentage and the unit price.

Recommendations

•Split irregular spaces into rectangles and add the sections.
•Add waste before ordering: x1.10 flooring, x1.15 tile, x1.20 diagonal.
•Measure twice and keep a photo record of large jobs.
•Re-run with worst-case dimensions so the order covers the whole job.

Educational Content

Introduction

Area is the two-dimensional space inside a boundary, expressed in square feet, square yards or square meters. In construction it sizes flooring, paint, tile, sod and concrete, and it underpins price-per-square-foot comparisons in real estate.

Concept Explanation

The area of a regular polygon is n × s² ÷ (4 × tan(π ÷ n)), where n is the number of equal sides and s is the side length. Unit conversion always happens before the formula is applied, so mixing feet and inches can never silently corrupt the result. Multiply by quantity for repeated rooms, then add the trade waste factor to get the order quantity.

Applications

▸Flooring, tile, carpet and paint ordering with waste allowances

▸Real-estate area checks and price-per-square-foot comparison

▸Concrete, sod, mulch and paver quantity takeoffs

▸Wall and ceiling coverage for drywall, primer and texture

▸Bids and change orders priced per square foot

Benefits

•One live number for net area, conversions, waste and cost
•Exact conversions to sq yd, sq m and acres
•Waste and cost plans generated from the same inputs
•Step-by-step working you can attach to a bid

Limitations

•Flat-area geometry only — roof pitch and wall height are not added
•Paint needs wall area (perimeter times height), not floor area
•Appraisal living-area rules are explained but not enforced

Best Practices

•Measure wall-to-wall for interiors, exterior-to-exterior for footprints
•Keep one unit throughout; convert inches to feet first
•Measure twice and photograph the tape for large jobs
•Add the trade waste factor before ordering, not after

Common Misconceptions

Myth: Ordering the exact measured area is enough.

Truth: Cuts, offcuts and breakage consume 10–20%. Ordering net guarantees a second trip.

Myth: Length times width works for every room.

Truth: It works for rectangles only — split L-shaped or angled rooms into rectangles, triangles and circles, then add.

Myth: Square footage and price per square foot tell the whole story.

Truth: Finish level, ceiling height and waste move the real cost far more than the bare area.

Practical Tips

•Split irregular spaces into rectangles and add the sections.
•Add waste before ordering: x1.10 flooring, x1.15 tile, x1.20 diagonal tile.
•Measure twice — laser measurers beat tapes past about 20 ft.
•Enter your actual price per unit to turn the area into a budget in one step.

Common Mistakes

Mixing feet and inches in one calculation.

Pick one unit in the dropdown — conversion is applied to every field automatically.

Ordering the net area with no waste allowance.

Use the order quantity row: net times 1.10 for flooring, 1.15 for tile.

Measuring the wrong face of the wall.

Interiors are wall-to-wall; building footprints are exterior-to-exterior.

Forgetting repeated rooms.

Use Quantity for identical rooms instead of re-running the calculator.

Assumptions

This calculator makes the following assumptions to provide estimates:

Flat plane: Area is measured on a flat plane; slope and pitch are not added.

Consistent unit: All inputs share the selected unit and are converted once.

Rectangular model: The shape matches the selected geometry; split complex rooms first.

Limitations

Be aware of these limitations when using this calculator:

Not an appraisal: Living-area rules (ceiling height, egress, above-grade) are explained but not enforced.

Estimates, not quotes: Cost rows use allowances and your unit price — get 2–3 local quotes.

Frequently Asked Questions

Answers to common questions about this calculator.

How do I calculate the area of a regular polygon?

Use A = n × s² ÷ (4 × tan(π ÷ n)) with n equal sides of length s. A regular hexagon with 4 ft sides is about 41.57 sq ft.

What is a regular polygon?

A flat shape with all sides and all angles equal — equilateral triangle, square, regular hexagon and so on. Irregular shapes need splitting into simpler pieces.

How do I measure with feet and inches?

Convert inches to feet by dividing by 12, then multiply. Example: 12 ft 6 in x 10 ft 3 in = 12.5 x 10.25 = 128.13 sq ft. Select Inches as the unit and the conversion is automatic.

What is the difference between net area and order quantity?

Net area is what you measure. Order quantity is net plus the waste allowance — the number the supplier invoice should match.

How do I convert square feet to square yards or square meters?

Divide square feet by 9 for square yards or by 10.764 for square meters. The results dashboard shows every conversion live.

How do I handle an L-shaped or irregular room?

Split it into rectangles, calculate each section, then add them up. Use Quantity for repeated identical sections.

What does the price per square foot include?

Whatever unit price you enter — material only, or an all-in rate. The cost plan labels which unit the price applies to.

How accurate is this calculator?

Every figure follows directly from the inputs using standard geometry, so it is accurate to the quality of your measurements. Verify on site before ordering.

How do I measure a room that is not a perfect rectangle?

Split it into rectangles (plus triangles or circles for angled or curved parts), measure each section, and add them. The Irregular Area Calculator adds sections for you.

Wall-to-wall or exterior-to-exterior — which do I measure?

Wall-to-wall for interiors like flooring and paint; exterior-to-exterior for footprints, concrete and roofing. Using the wrong face is a classic 5% error.

How do I convert polygon area calculator results to square yards?

Divide square feet by 9. Flooring, carpet and concrete are often priced per square yard, so the results dashboard shows it live.

How many square feet are in an acre?

43,560 sq ft (about 4,047 sq m). Lots and land sod, seed and grading quantities usually start from acreage.

Do closets, halls and stairs count in floor area?

For material ordering, yes — cover everything. For real-estate living area, appraisers follow ANSI rules that exclude garages, unfinished space and porches.

How much extra flooring should I order over the net area?

10% for laminate, vinyl and carpet; 15% for tile; 20% for diagonal or patterned layouts. Keep one spare box for repairs.

How do I estimate paint from floor area?

You need wall area instead: room perimeter times wall height, minus about 15 sq ft per window and 20 per door. One gallon covers roughly 350 sq ft per coat.

What is price per square foot really telling me?

Cost divided by area — useful for comparing bids and listings, but finish level, ceiling height and waste move the real number more than the bare area.

How do I measure stairs, slopes or curved walls for area?

Break them into flat rectangles and triangles, or measure the developed (unrolled) length times width. Never guess curves — segment them.

Should I deduct for fixtures, cabinets and islands?

For flooring under wall-hung or built-in items, deduct large permanent footprints; for paint and ceiling work, deduct nothing. When in doubt, keep the area — spare material is cheap.

How does ceiling height affect material estimates?

Floor area stays the same, but wall area, paint, drywall and trim all scale with height. Re-run wall-based tools when ceilings are not 8 ft.

What is gross vs net vs rentable area?

Gross is everything inside the exterior walls; net/usable is space you occupy; rentable adds your share of common areas. Material orders use net plus waste.

What if my site conditions differ from the page defaults?

Defaults are worked examples, not recommendations — replace every input with your own measurements, prices and allowances before ordering or bidding.

How do I budget for price changes mid-project?

Lock supplier quotes in writing with expiry dates, carry a 5–10% escalation contingency, and re-run the calculator when prices move. Volatile materials get shorter quote windows.

Should I buy materials in bulk for this job?

Bulk wins when storage is dry and secure, the material keeps, and the discount beats carrying cost. Otherwise phased delivery avoids damage, theft and cash lockup.

How do I document quantities for change orders?

Record before-and-after measurements with dated photos, keep delivery tickets, and re-run the calculator for the changed scope. Paper trails get paid; memories do not.

What inspections relate to the polygon area calculator?

Anything structural, concealed or regulated gets inspected before covering: footings, steel, drains, waterproofing and rough-ins. Book inspections before the work that buries them.

How do I measure correctly for the polygon area calculator?

Measure twice with a tape or laser, write every reading down before typing it in, and keep one unit throughout. Photos of the tape protect you on disputed dimensions.

What units does the polygon area calculator use?

Whatever unit you select — pick one and use it for every field so conversions stay consistent. Results convert to the common trade units automatically.

How accurate is the polygon area calculator?

Exact for the numbers entered: all math runs at full precision and rounds only for display. Field accuracy depends on your measurements, so verify critical dimensions on site.

Can I use the polygon area calculator for bids and quotes?

Yes — the steps section shows the full working, and the breakdown table lists order quantities. Attach both to bids so clients see net figures and allowances separately.

Should I add waste or contingency to the result?

Yes. Add the trade waste factor (5–20% depending on material) before ordering, and carry a separate 5–10% budget contingency for price movement and surprises.

Related Calculators

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Related Guides

Deepen your understanding with these educational resources.

Measuring rooms for flooring and paint

Wall-to-wall vs exterior-to-exterior, and which number each trade needs.

Polygon Area Calculator worked examples

Step-by-step polygon area calculator examples with real job-site numbers.

Measurement & Dimensions estimating tables

Reference tables, waste factors and coverage rates for measurement & dimensions.

Glossary

Technical terms used in mortgage calculations explained in plain language.

Square foot (sq ft): Area of a 1 ft x 1 ft square. 144 sq in = 1 sq ft; 9 sq ft = 1 sq yd.
Net area: Measured area before any waste allowance is added.
Order quantity: Net area plus the waste factor — the quantity to buy.
Waste factor: Extra material for cuts and errors, typically 10–20%.
Takeoff: Measuring quantities from plans or dimensions for ordering.
sq ft: The primary area unit reported by this calculator.

Authoritative References

Trusted sources and standards referenced by this calculator.

NIST — SI Unit Conversion Factors ANSI — Measurement Standards (Z765) International Code Council — IRC USGS — Mapping & Measurement Science

Applicable Standards

1 acre = 43,560 sq ft · 1 sq yd = 9 sq ft · 1 sq m = 10.764 sq ftMeasure residential area to the nearest 1/10 ft (ANSI Z765 guidance)Money rounded for display only; all calculations run at full precisionVerify dimensions on site before ordering materials

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Page Information

Last Updated:

2026-09-23

Version:

2.0.0

References:

License:

Free to use for educational and professional purposes.