Amogh N P
✦ In loving memory of Amogh N P — Architect · Designer · Visionary ✦
A building of pure stacked volumes — area and volume made visible.
Unit III25ART102 · Mathematics in Architecture

Area & Volume Calculations

Measuring space — from carpet area to concrete and water tanks.

≈ 35 min · live calculator

This is the maths you will use every single day in practice. How big is the floor? How much will the flat “sell” as? How much concrete, how many litres? It all comes down to area and volume — so let's make them second nature, with a live calculator.

Learning objectives

By the end of this lesson, you will be able to — mapped to the course outcomes for Building Materials & Construction I:

1
CO3 · Apply

Calculate the area of plan shapes and approximate irregular plots.

2
CO3 · Understand

Distinguish carpet, built-up and super built-up area, and compute FAR/FSI.

3
CO3 · Apply

Calculate volumes and surface areas of the common solids.

4
CO3 · Apply

Use these in quantity take-off — concrete, water tanks, finishes.

Measuring the plan

Area — and what counts as 'area'

First the shapes; then the surprisingly tricky question of which area — carpet, built-up or super built-up — and the FAR that limits how much you can build.[3]

Area — the shapes you measure most RectangleA = l × b TriangleA = ½ b h CircleA = π r² TrapeziumA = ½(a+b) h For an irregular plot, the trapezoidal & Simpson's rules sum strips of these shapes (surveying).
DiagramArea formulas for rectangle, triangle, circle and trapezium
Carpet vs built-up vs super built-up Carpet area net usable floor + walls, balcony = built-up area + share of common = super built-up RERA (2016) defines carpet area as the net usable floor area within the inner walls. FAR = total floor area ÷ plot area.
DiagramCarpet, built-up and super built-up area shown as nested regions
A dimensioned plan — every area statement starts here.
PhotoA dimensioned plan — every area statement starts here.
Measuring the solid

Volume & surface area

Add a third dimension and you can size concrete, water tanks and finishes. Enter a room's dimensions below to get its floor area, volume, wall area and capacity at once.

Volume — from rooms to water tanks Cuboidl·b·h Cylinderπ r² h Cone⅓ π r² h Sphere4⁄3 π r³ Pyramid⅓ · base · h 1 cubic metre = 1000 litres — a 2 × 1 × 0.75 m tank holds 1500 L.
DiagramVolume formulas for cuboid, cylinder, cone, sphere and pyramid
Try it

Room area, volume & surface area

Floor area
0.0 m²
Volume
0.0 m³
Wall area
0.0 m²
Capacity
0 L

Floor = l×b · Volume = l×b×h · Wall = 2(l+b)×h · Total surface = 66.0 m² · 1 m³ = 1000 L.

In practice

Where the maths is used

Select an application.

Carpet · built-up · super built-up

Carpet area is the net usable floor area within the inner walls (RERA, 2016); built-up adds walls and balconies; super built-up adds a share of common areas.[3]

An overhead water tank — capacity is just volume × 1000.
PhotoAn overhead water tank — capacity is just volume × 1000.
A slab being poured — volume becomes a quantity to estimate.
PhotoA slab being poured — volume becomes a quantity to estimate.
Check your understanding

Self-assessment

1. The area of a circle of radius r is:

2. One cubic metre of water equals how many litres?

3. Floor Area Ratio (FAR) is:

In a nutshell

Recap

Know the area formulas — rectangle, triangle, circle, trapezium — and how to strip an irregular plot.
Carpet < built-up < super built-up area; FAR = total floor area ÷ plot area.
Volume and surface-area formulas drive concrete, tank and finish quantities.
1 m³ = 1000 litres; areas are taken off per m², volumes per m³.
The evidence

References & further reading

  1. [1]Areas of plane shapes and Heron's formula. Wikipedia. https://en.wikipedia.org/wiki/Heron%27s_formula
  2. [3]RERA (2016) Section 2 — definition of carpet area; built-up vs super built-up. https://ibclaw.in/section-2-of-real-estate-regulation-and-development-act-2016-rera-definitions/
  3. [4]Floor area ratio (FAR / FSI). Wikipedia. https://en.wikipedia.org/wiki/Floor_area_ratio
  4. [5]Dutta, B.N. Estimating and Costing in Civil Engineering — mensuration & quantity take-off. https://books.google.com/books/about/Estimating_and_Costing_in_Civil_Engineer.html?id=QHHWAQAACAAJ
  5. [6]Measurement of area & volume — trapezoidal and Simpson's rules (surveying). https://esenotes.com/measurement-of-area-and-volume-mid-ordinate-rule-average-offset-rule-trapezoidal-rule-simpsons-rule/

Further reading

  • Dutta, B.N. & Dutta, S. Estimating and Costing in Civil Engineering: Theory and Practice. New Delhi: CBS Publishers.
  • A standard mensuration / quantity-surveying reference.

Sources gathered and fact-checked June 2026. Published values vary by source, sample and method — treat as indicative and confirm against the cited standard before structural use.