CBSE Class 7 Maths Formulas are the foundation for advanced topics in algebra, geometry, and mensuration. Mastering these formulas helps students solve sums faster and prepare effectively for school exams, Olympiads, and future CBSE board exams. This 2025 updated list includes all essential formulas from the NCERT syllabus.
Important CBSE Class 7 Maths Formulas
Mathematics in Class 7 introduces key ideas such as integers, rational numbers, algebraic expressions, geometry, and mensuration. Remembering formulas saves time during exams and builds confidence. Below you’ll find chapter-wise formulas explained with meaning and examples.
Arithmetic Formulas
| Concept | Formula | Explanation |
|---|---|---|
| Whole Numbers | \(a \times 0 = 0,\ a \times 1 = a\) | Multiplying any number with 0 gives 0; with 1 gives the same number. |
| Properties of Integers | Commutative: \(a+b=b+a\), Associative: \((a+b)+c=a+(b+c)\) | Order of addition and grouping doesn’t affect result. |
| Rational Numbers | \(\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}\) | Formula to add two rational numbers. |
| Average | \(\text{Average} = \frac{\text{\Sum of observations}}{\text{Number of observations}}\) | Used to find mean value. |
| Percentage | \(\text{Percentage} = \frac{\text{Value}}{\text{Total Value}} \times 100\) | Represents part per hundred. |
| Simple Interest | \(SI = \frac{P \times R \times T}{100}\) | P = Principal, R = Rate, T = Time. |
| Profit & Loss | Profit = SP – CP, Loss = CP – SP | SP = Selling Price, CP = Cost Price. |
| Discount | \(\text{Discount} = \frac{\text{Discount %} \times \text{Marked Price}}{100}\) | Used in commercial arithmetic problems. |
Algebra Formulas
Algebra introduces variables and equations. Below are the most used formulas in Class 7 and higher classes:
| Formula Type | Formula | Use |
|---|---|---|
| Square of Sum | \((a + b)^2 = a^2 + 2ab + b^2\) | Expanding expressions. |
| Square of Difference | \((a – b)^2 = a^2 – 2ab + b^2\) | Used in simplifications. |
| Product of Sum & Difference | \((a + b)(a – b) = a^2 – b^2\) | Identity for difference of squares. |
| Cube of Sum | \((a + b)^3 = a^3 + b^3 + 3ab(a + b)\) | Helps expand cubic polynomials. |
| Cube of Difference | \((a – b)^3 = a^3 – b^3 – 3ab(a – b)\) | Used in algebraic factorization. |
| Sum of Cubes | \(a^3 + b^3 = (a + b)(a^2 – ab + b^2)\) | Used for factorization. |
| Difference of Cubes | \(a^3 – b^3 = (a – b)(a^2 + ab + b^2)\) | Common in algebraic simplifications. |
Geometry Formulas
Geometry deals with shapes, angles, and spatial understanding. Below are essential formulas for Class 7 Geometry:
| Shape | Formula | Meaning |
|---|---|---|
| Perimeter of Rectangle | \(P = 2(l + b)\) | l = length, b = breadth. |
| Area of Rectangle | \(A = l \times b\) | Used for finding surface coverage. |
| Perimeter of Square | \(P = 4a\) | a = side. |
| Area of Square | \(A = a^2\) | Square region formula. |
| Area of Triangle | \(A = \frac{1}{2} \times b \times h\) | b = base, h = height. |
| Perimeter of Triangle | \(P = a + b + c\) | Sum of all sides. |
| Area of Parallelogram | \(A = b \times h\) | b = base, h = height. |
| Area of Circle | \(A = \pi r^2\) | r = radius; π = 3.14 or \(\frac{22}{7}\). |
| Circumference of Circle | \(C = 2\pi r\) | Distance around the circle. |
Mensuration Formulas
Mensuration covers both 2D (plane figures) and 3D (solid shapes). These are frequently used in exams:
| Shape | Formula | Explanation |
|---|---|---|
| Perimeter of a Circle | \(2\pi r\) | Also known as circumference. |
| Area of Trapezium | \(A = \frac{1}{2}(a + b)h\) | a, b = parallel sides; h = height. |
| Area of Rhombus | \(A = \frac{1}{2} \times d_1 \times d_2\) | d₁, d₂ = diagonals. |
| Volume of Cuboid | \(V = l \times b \times h\) | Product of dimensions. |
| Volume of Cube | \(V = a^3\) | a = side length. |
| Surface Area of Cuboid | \(2(lb + bh + hl)\) | Sum of all faces. |
| Surface Area of Cube | \(6a^2\) | Six equal faces of square area. |
| Volume of Cylinder | \(V = \pi r^2 h\) | Used for 3D solid with circular base. |
| Curved Surface Area of Cylinder | \(A = 2\pi r h\) | Excluding top and bottom circles. |
Data Handling Formulas
| Concept | Formula | Description |
|---|---|---|
| Mean (Average) | \(\bar{x} = \frac{\sum x}{n}\) | Sum of all data ÷ number of observations. |
| Mode | Value with maximum frequency | Most occurring observation. |
| Median | Middle value of arranged data | Separates higher and lower halves. |
Worked Examples
Example 1: Find the area of a triangle with base 10 cm and height 8 cm.
\(A = \frac{1}{2} \times b \times h = \frac{1}{2} \times 10 \times 8 = 40\,\text{cm}^2\)
Example 2: Calculate simple interest on ₹5000 at 10% per annum for 2 years.
\(SI = \frac{P \times R \times T}{100} = \frac{5000 \times 10 \times 2}{100} = ₹1000\)
Example 3: A square field has side 12 m. Find its area and perimeter.
\(A = a^2 = 12^2 = 144\,\text{m}^2;\quad P = 4a = 48\,\text{m}\)