Area Calculator & Geometry Formula Guide
An area calculator is one of the most used mathematical tools in school, college, and professional work. Whether you are calculating the floor space of a room in Nepal, working out the surface area of a construction plot, or solving LCM and GCF problems for a competitive exam, having a reliable area formula calculator and an online geometry tool saves time and eliminates errors. NepaCalc's Geometry Studio combines all these functions in a single, interactive workspace.
Complete Area Formula Reference
The following table covers every major shape with its area formula. These are the same formulas used in the curriculum of Nepal's NEB (National Examinations Board) for Classes 9 through 12.
| Shape | Area Formula | Variables |
|---|---|---|
| Square | A = s² | s = side length |
| Rectangle | A = l × w | l = length, w = width |
| Triangle | A = ½ × b × h | b = base, h = height |
| Circle | A = π × r² | r = radius |
| Parallelogram | A = b × h | b = base, h = perpendicular height |
| Trapezoid | A = ½(a + b) × h | a, b = parallel sides, h = height |
| Rhombus | A = ½ × d₁ × d₂ | d₁, d₂ = diagonals |
| Ellipse | A = π × a × b | a = semi-major, b = semi-minor axis |
| Regular Hexagon | A = (3√3/2) × s² | s = side length |
| Triangle (Heron's) | A = √(s(s−a)(s−b)(s−c)) | s = semi-perimeter, a,b,c = sides |
LCM (Least Common Multiple)
The LCM of two or more numbers is the smallest positive integer that is divisible by each of those numbers. It is used in adding fractions with different denominators, scheduling repeating events, and solving gear ratio problems.
Example: LCM(12, 18) = (12×18)/6 = 36
GCF (Greatest Common Factor)
The GCF (also called GCD for Greatest Common Divisor) is the largest number that divides all given numbers without a remainder. It is used in simplifying fractions, dividing items into equal groups, and in the Euclidean algorithm.
Example: GCF(12, 18) = GCF(18, 12) = GCF(12, 6) = 6
Methods to Calculate LCM and GCF
Our calculator for LCM and GCF uses the most efficient algorithm known as the Euclidean method. Here is how the major methods compare.
| Method | Best For | Speed |
|---|---|---|
| Listing Multiples | Small numbers (below 50) | Slow |
| Prime Factorization | Medium numbers, educational clarity | Medium |
| Euclidean Algorithm | Any size numbers, programming | Fast |
| Division Method | Multiple numbers at once | Efficient |
Perimeter Formulas for All Major Shapes
| Shape | Perimeter Formula | Notes |
|---|---|---|
| Square | P = 4s | All sides equal |
| Rectangle | P = 2(l + w) | Two pairs of equal sides |
| Triangle | P = a + b + c | Sum of all three sides |
| Circle | C = 2πr | Circumference, r = radius |
| Regular Polygon | P = n × s | n = number of sides, s = side length |
Real-World Uses of the Area Formula Calculator
Construction in Nepal
Contractors calculate floor area (in square feet) to estimate cost of tiles, cement, and flooring. A standard room of 12×14 ft has an area of 168 sq ft. Our tool computes this instantly.
Agriculture & Land
Farmers use area calculations to estimate crop yield. A circular field with radius 50m has area = π×50² ≈ 7,854 m². Combined with our Land Converter, this gives acreage in local units too.
SEE & NEB Exams
Area and perimeter problems are standard in Nepal's SEE math exam. LCM and GCF are tested heavily in Class 9 and 10. Our LCM GCF calculator is used by thousands of Nepali students daily.
Frequently Asked Questions
What is the LCM of 4 and 6?
LCM(4, 6) = 12. Using prime factorization: 4 = 2², 6 = 2×3. LCM = 2² × 3 = 12.
What is the GCF of 24 and 36?
GCF(24, 36) = 12. Factors of 24: 1,2,3,4,6,8,12,24. Factors of 36: 1,2,3,4,6,9,12,18,36. Largest common = 12.
How do I calculate the area of an irregular shape?
Use the Shoelace Formula: A = ½|Σ(xᵢ × yᵢ₊₁ − xᵢ₊₁ × yᵢ)|. Our geometry canvas calculates this automatically as you place points.
What is the difference between area and perimeter?
Area measures the 2D space inside a shape (in square units). Perimeter measures the total boundary length around a shape (in linear units).
Is LCM always larger than GCF?
Yes, for numbers greater than 1, LCM ≥ GCF. And LCM × GCF = product of the two numbers. For equal numbers a, LCM = GCF = a.
Can I calculate area in Ropani or Bigha?
Yes! After finding the area in square feet, use our Nepal Land Converter to convert to Ropani, Aana, Bigha, or Kattha for real estate transactions.