How Many Tiles to Cover a Floor

📑 On this page

⚡ The short answer

Number of tiles = floor area ÷ one tile's area, both in the same unit. That works when tiles can be cut or the sides divide evenly. For things that stay whole (chairs, stalls, cartons), count along each side instead: ⌊L ÷ l⌋ × ⌊B ÷ b⌋. The classic trap: forgetting to square the unit conversion.

🎬 The 30-second story

The fest that sold 31 stalls

“Ground: 20 m by 14 m. Stalls: 3 m by 3 m. How many can I rent?”

🎪

Kabir

Kabir runs the stalls at the college fest.

“280 ÷ 9 = 31.1. Sell 31.”

🧮

Aarav

Aarav divides area by area in four seconds.

“Why do I have 24 stalls and seven angry vendors?”

📏

Kabir

Fest morning. The tape measure disagrees.

“Six fit along 20 m, four along 14 m. Six fours are 24.”

🧱

Zoya

The two leftover strips are 2 m wide. No 3 m stall fits.

Tara's maths: Area ÷ area assumes you can chop stalls up to fill every gap. You can't. Count along each side, drop the decimals, multiply: 6 × 4 = 24.

How do you calculate how many tiles cover a floor?

Think of the floor as a sheet and each tile as a sticker. Tiles don't overlap and leave no gaps, so each one claims its own patch. All the patches together make the floor. Flip that: floor area ÷ one tile's area = number of tiles. That's the whole idea. The rest of this page is about when it breaks.

🧮 The formula

The counting formula

🟫

Floor area

L × B

🔲

One tile's area

same unit

🔢

Number of tiles

round up to buy

📐 The figure

Same unit before you divide

Kitchen floor

360 cm × 240 cm

Convert to cm before multiplying.

One tile

Area = 600 cm²

12 along each side: 144 tiles.

Figures are not to scale.

There's a faster route to the same number. Count tiles along the length, count along the breadth, multiply. Here 360 ÷ 30 = 12 and 240 ÷ 20 = 12, so 144. No big numbers. When the sides divide evenly, both routes always agree.

When does floor area ÷ tile area give the wrong answer?

When the sides don't divide evenly and the pieces can't be cut. A tile can be sliced to fill the strip by the wall. A chair, a stall or a carton can't. The leftover strips stay empty, so area ÷ area overcounts. Kabir's area said 31; his ground held 24.

⚔️ Side by side

Two ways to count

📐Area method

floor area ÷ item area

•Items can be cut: tiles, carpet, turf
•Or every side divides evenly
•Gives the ceiling: never more than this

🧱Fit method

⌊L ÷ l⌋ × ⌊B ÷ b⌋

•Items stay whole: chairs, stalls, boxes
•Drop the decimal on each side, then multiply
•Try the item both ways round

Test	Area method	Fit method
Stalls on Kabir's ground	31.1 (wrong)	6 × 4 = 24
Kitchen tiles	144	12 × 12 = 144

⚠️ Turn it round before you trust it

A 2 ft × 2.5 ft chair on an 18 ft × 12 ft floor fits 9 × 4 = 36 one way and 7 × 6 = 42 the other. Mix the two layouts and you reach 43. CLAT asked exactly this in 2020.

🧭 Decision flow

Which method do I use?

❓ Can the items be cut to fit?

tiles, carpet, grass

Yes →

Area ÷ area. Round up if buying.

No ↓

❓ Does each side divide evenly?

Yes →

Either method. They match.

No ↓

❓ Is the item a square?

Yes →

⌊L ÷ s⌋ × ⌊B ÷ s⌋.

No →

Fit method both ways round, then check the options.

How do you solve tiling questions step by step?

✍️ Worked example Warm-up ⏱ 40 sec

The kitchen floor

Meher's kitchen is 3.6 m by 2.4 m. Tiles are 30 cm by 20 cm. How many tiles, with no cutting?

1
Same unit: 360 cm by 240 cm.
2
Along the length: 360 ÷ 30 = 12. Along the breadth: 240 ÷ 20 = 12.
3
12 × 12 = 144. Area check: 86,400 ÷ 600 = 144.

Answer: 144 tiles

⚡ The exam-hall shortcut

With friendly numbers, divide side by side. 12 × 12 is mental maths; 86,400 ÷ 600 isn't.

✍️ Worked example CLAT level ⏱ 75 sec

The largest square tile

A dance studio is 10.5 m by 6.3 m. Zoya wants identical square tiles, as large as possible, with no cutting. How many?

1
No cutting means the tile's side divides both sides exactly. Largest such side = HCF.
2
HCF(1050 cm, 630 cm) = 210 cm.
3
1050 ÷ 210 = 5 and 630 ÷ 210 = 3, so 5 × 3 = 15 tiles.

Answer: 15 tiles of 2.1 m

⚡ HCF shortcut

Largest square tile = HCF of the sides. Fewest tiles = (L ÷ HCF) × (B ÷ HCF).

✍️ Worked example CLAT level ⏱ 80 sec

Paving the path round a lawn

A lawn is 12 m by 8 m. A 1 m wide path runs round it, outside. How many 50 cm × 50 cm tiles pave the path?

1
Lawn plus path = (12 + 2) by (8 + 2) = 14 m by 10 m. The width adds on both sides.
2
Path = 140 − 96 = 44 m².
3
One tile = 0.25 m², so 44 ÷ 0.25 = 176.

Answer: 176 tiles

⚡ The exam-hall shortcut

Outer minus inner, always. 'Perimeter × width' gives 40 m² and 160 tiles: it loses the four corner squares.

✍️ Worked example Tricky ⏱ 2 min

Cartons in a van

Kabir's van holds a space 2.1 m × 1.5 m × 1 m. How many 40 cm × 30 cm × 20 cm cartons fit?

1
Volume says 3,150,000 ÷ 24,000 = 131.25. That's the ceiling, not the answer.
2
Cartons don't bend, so count per edge: 40 along 210, 30 along 150, 20 along 100 gives 5 × 5 × 5 = 125.
3
Other turns do worse (105 at best). The spare 10 cm slab is thinner than any carton side.

Answer: 125 cartons

⚡ The exam-hall shortcut

In 3D: ⌊L ÷ l⌋ × ⌊B ÷ b⌋ × ⌊H ÷ h⌋. Match each carton side to the edge it divides most cleanly.

What is the fastest way to count tiles in the exam?

1
Fix one unit
1 m = 100 cm, but 1 m² = 10,000 cm². 1 ft = 12 in, but 1 sq ft = 144 sq in.
2
Divide side by side
Whole numbers? Multiply and stop. Decimals? Ask whether the item can be cut.
3
Round the right way
Buying to cover: round up. Fitting inside: round down.
4
Let the options vote
The area answer is the ceiling. Strike any option above it.

🎛️ Try it yourself — change any number

Try it: chairs on the 2020 CLAT floor

Room length (ft) Room breadth (ft) Chair length (ft) Chair breadth (ft)

By area

43.2

Whole tiles that actually fit (no cutting)

216 ÷ 5 = 43.2 — check the sides divide evenly

Area says 43.2; this layout fits 36. Swap the chair to 2.5 by 2 and it jumps to 42. Then try Kabir's ground: 20, 14, 3, 3.

💡 Boxes round up too

Need 176 tiles, sold in boxes of 10? Buy 18 boxes, not 17.6. Round once, at the end, in the direction the real world forces.

How does CLAT hide tiling inside a caselet?

CLAT 2020 gave a room, a chart of five objects and five questions. The word 'tiling' never appeared. They asked about uncovered floor, free table top, and how many tables or chairs would carpet the floor. Each is one idea: a footprint is length × breadth. Heights are noise unless you're filling space.

Object	Length × breadth	Footprint	Used in
Room floor	18 ft × 12 ft	216 sq ft	Q141, 143, 145
Bed	3.5 ft × 6 ft	21 sq ft	Q141
Table	3 ft × 4 ft	12 sq ft	Q141–143
Chair	2 ft × 2.5 ft	5 sq ft	Q141, 145
Book (×3)	12 in × 6 in	72 sq in	Q142

→ scroll to see more

🥧 The split

Where the 216 sq ft of floor goes

Uncovered178 sq ft
Bed21 sq ft
Table12 sq ft
Chair5 sq ft

📌 Things on top take no extra floor

The books and lamp sit on the table. They use table-top area, not floor area. Subtract them from the floor and you land on a planted wrong option.

What are the common traps in tiling questions?

✓Unsquared conversion. A 9 in tile is 0.75 ft, so its area is 0.5625 sq ft, not 0.75.
✓Missing corners. A path outside a rectangle is outer − inner.
✓Circles. A round base takes πr², not (2r)².
✓Wrong rounding. 43.2 chairs is 43; 175.2 tiles to buy is 176.
✓'Data inadequate' bait. Extra data, like height, doesn't make a question unsolvable.

How did CLAT ask it? The 2020 room caselet

📝 Asked in CLAT 2020 · Q141 Uncovered floor

A room having the dimensions as mentioned in the chart below has a table, a bed and a chair. There are three books kept on the table (side by side) and also a lamp having radius, 3.5 inch. Room: 18 feet × 12 feet × 12 feet Bed: 3.5 feet × 6 feet × 3 feet Table: 3 feet × 4 feet × 4 feet Chair: 2 feet × 2.5 feet × 4 feet Books: 12 inch × 6 inch × 3 inch (length × breadth × height)

What would be the area of the room which is not covered by any object as mentioned above?

A176.5 sq. ft.

B178 sq. ft.

C367 sq. ft.

D245.5 sq. ft.

Reveal answer + reasoning

Answer: B

Floor = 18 × 12 = 216 sq ft. Footprints: bed 21 + table 12 + chair 5 = 38. Books and lamp are on the table. 216 − 38 = 178 sq ft. About 45 seconds.

Why the others fail

A — Also subtracts the three books (1.5 sq ft), which are on the table.
C — More than the whole floor. Impossible.
D — Also more than 216. Impossible.

📝 Asked in CLAT 2020 · Q142 Free table top

…There are three books kept on the table (side by side) and also a lamp having radius, 3.5 inch… Table: 3 feet × 4 feet × 4 feet Books: 12 inch × 6 inch × 3 inch (length × breadth × height)

What is the area of the table which is uncovered by any of the objects?

A1656 sq. inch

B1617.52 sq. inch

C1473.52 sq. inch

D1512 sq. inch

Reveal answer + reasoning

Answer: C

Table top = 36 in × 48 in = 1,728 sq in. Books = 3 × 72 = 216. Lamp base = π × 3.5² ≈ 38.48. Free = 1,728 − 216 − 38.48 = 1,473.52 sq in. About 70 seconds. Shortcut: 1,728 − 216 = 1,512 is option D; the answer is about 38 less, and only C is.

Why the others fail

A — Counts one book and no lamp.
B — One book plus the lamp. There are three books.
D — Three books, but the lamp is forgotten.

📝 Asked in CLAT 2020 · Q143 How many fit

A room having the dimensions as mentioned in the chart below has a table, a bed and a chair… Room: 18 feet × 12 feet × 12 feet Table: 3 feet × 4 feet × 4 feet (length × breadth × height)

How many tables are required to cover the floor surface of the room completely?

A18

B11

C21

DData inadequate.

Reveal answer + reasoning

Answer: A

216 ÷ 12 = 18. Fit check: 18 ÷ 3 = 6 and 12 ÷ 4 = 3, so 6 × 3 = 18 with no gap. About 20 seconds.

Why the others fail

B — No clean division of 216 gives 11.
C — The bed's footprint, lying in your rough work.
D — Both footprints are given. Heights are extra, not missing.

📝 Asked in CLAT 2020 · Q145 Chairs on the floor

A room having the dimensions as mentioned in the chart below has a table, a bed and a chair… Room: 18 feet × 12 feet × 12 feet Chair: 2 feet × 2.5 feet × 4 feet (length × breadth × height)

How many chairs can be put inside the room so as to cover the entire floor area of the room?

A40

B21

C43

D18

Reveal answer + reasoning

Answer: C

216 ÷ 5 = 43.2, so 43. It really fits: on 10 ft of the breadth, 9 chairs per row × 4 rows = 36; the last 18 ft × 2 ft strip takes 7 chairs turned round. 36 + 7 = 43. About 30 seconds. The key treats the floor as empty.

Why the others fail

A — 43 fit, so 40 isn't the most.
B — The bed's area again.
D — The table count from Q143. Smaller chairs must fit more.

💥 Myth vs fact

Tiling myths that cost marks

🙅 Myth

Area ÷ area always gives the count.

Tap to bust it →

✅ Fact

Only if items can be cut or sides divide evenly. Kabir's ground: 31 by area, 24 in reality.

🙅 Myth

1 m² = 100 cm².

Tap to bust it →

✅ Fact

Square the factor: 10,000 cm². And 1 sq ft = 144 sq in.

🙅 Myth

Path area = perimeter × width.

Tap to bust it →

✅ Fact

That drops the corners. Outer − inner: 44 m², not 40.

🙅 Myth

Round to the nearest whole number.

Tap to bust it →

✅ Fact

Buying: round up. Fitting: round down.

🎯 Quick quiz

Five floors, five counts

0 / 5

Q1. A 5 m × 3 m balcony, tiles 25 cm × 20 cm. How many tiles?

Q2. Least number of identical square tiles, no cutting, for a 7.2 m × 4.8 m hall?

Q3. How many whole 3 ft × 3 ft mats fit in rows on a 10 ft × 8 ft floor?

Q4. A 2 m deck runs round a 20 m × 15 m pool. At ₹150 per m², what does it cost?

Q5. How many 9-inch square tiles cover a 15 ft × 12 ft room?

🎯 Tiling in a nutshell

Count = floor area ÷ item area, in one unit.
Whole items: ⌊L ÷ l⌋ × ⌊B ÷ b⌋, both ways round.
Largest square tile = HCF of the sides.
Paths: outer − inner.
Round up to buy, down to fit.

📎 Formula card

Tiles = (L × B) ÷ (l × b)
Whole items = ⌊L ÷ l⌋ × ⌊B ÷ b⌋ (3D: × ⌊H ÷ h⌋)
Largest square tile = HCF(L, B); count = LB ÷ HCF²
Outside path, width w = (L + 2w)(B + 2w) − LB
Inside path = LB − (L − 2w)(B − 2w)
1 m² = 10,000 cm²; 1 sq ft = 144 sq in
Cost = tiles × price per tile

Frequently asked questions

How do you calculate the number of tiles needed for a floor?

Put the floor and one tile in the same unit, then divide area by area. A 3.6 m by 2.4 m floor with 30 cm by 20 cm tiles needs 86,400 ÷ 600 = 144 tiles. Quicker: 360 ÷ 30 = 12 and 240 ÷ 20 = 12, so 12 × 12 = 144. Round up when you're buying.

How do you find the largest square tile for a room?

Take the HCF of the length and breadth in the same unit. That's the biggest square that fits with no cutting. For 10.5 m by 6.3 m, HCF(1050, 630) = 210 cm, so 2.1 m tiles, 5 × 3 = 15 of them.

How many 2 ft by 2 ft tiles cover a 10 ft by 12 ft room?

120 sq ft ÷ 4 sq ft = 30 tiles. By sides: 10 ÷ 2 = 5 and 12 ÷ 2 = 6, so 5 × 6 = 30, with no cutting. With 1 ft tiles you'd need 120.

Why do fewer objects fit than area divided by area?

Area ÷ area assumes gaps get filled with cut pieces. Chairs and boxes can't be cut, so narrow strips stay empty. A 20 m by 14 m ground holds 6 × 4 = 24 stalls of 3 m by 3 m, not 31. Count per side and drop decimals.