Class 6 Maths All Formulas: The Complete CBSE Formula Sheet (2026)

Indian place value system:

International place value system:

Conversions:

Estimation and rounding:
- Round to the nearest $10$: look at the ones digit. If $\ge 5$, round up.
- Round to the nearest $100$: look at the tens digit.
- Round to the nearest $1000$: look at the hundreds digit.

Roman numerals key values:
$I = 1$, $V = 5$, $X = 10$, $L = 50$, $C = 100$, $D = 500$, $M = 1000$

Memory tip: In the Indian system, commas are placed after the hundreds, then every two digits (e.g., 1,23,45,678). In the international system, commas are placed every three digits (e.g., 12,345,678).

Successor: $n + 1$ (the next number)
Predecessor: $n - 1$ (the previous number)

Closure property:

Commutative property:

Associative property:

Distributive property:

Identity elements:
- Additive identity: $a + 0 = a$
- Multiplicative identity: $a \times 1 = a$

Multiplication by zero: $a \times 0 = 0$

Division by zero: Not defined.

Memory tip: The distributive property is your best friend for mental maths. Use it to break hard multiplications: $7 \times 98 = 7 \times (100 - 2) = 700 - 14 = 686$.

Factors: Numbers that divide a given number exactly (remainder $0$).

Multiples: Products of a number with whole numbers.

Prime number: A number greater than $1$ with exactly two factors ($1$ and itself).

Composite number: A number greater than $1$ with more than two factors.

Note: $1$ is neither prime nor composite.

Prime factorisation: Every composite number can be expressed as a product of primes.

Example: $60 = 2^2 \times 3 \times 5$

HCF (Highest Common Factor): The largest factor common to two or more numbers.

LCM (Lowest Common Multiple): The smallest multiple common to two or more numbers.

Key relationship:

Example: Find HCF and LCM of $12$ and $18$.
$12 = 2^2 \times 3$ and $18 = 2 \times 3^2$
$\text{HCF} = 2^1 \times 3^1 = 6$
$\text{LCM} = 2^2 \times 3^2 = 36$
Check: $6 \times 36 = 216 = 12 \times 18$. Correct.

Divisibility rules:
- By $2$: last digit is even ($0, 2, 4, 6, 8$)
- By $3$: sum of digits is divisible by $3$
- By $4$: last two digits form a number divisible by $4$
- By $5$: last digit is $0$ or $5$
- By $6$: divisible by both $2$ and $3$
- By $9$: sum of digits is divisible by $9$
- By $10$: last digit is $0$
- By $11$: difference of sums of alternate digits is $0$ or divisible by $11$

Integers: $\ldots, -3, -2, -1, 0, 1, 2, 3, \ldots$

Absolute value: $|a|$ is the distance of $a$ from $0$ on the number line.

Addition rules:
- Same sign: Add absolute values, keep the common sign.

Subtraction: Add the additive inverse.

Ordering: On the number line, a number to the right is always greater.

Memory tip: Subtracting a negative is the same as adding a positive. "Minus a minus is a plus."

Types of fractions:
- Proper: numerator $<$ denominator (value $< 1$)
- Improper: numerator $\ge$ denominator (value $\ge 1$)
- Mixed: whole number + proper fraction

Converting mixed to improper:

Equivalent fractions:

Simplest form: Divide numerator and denominator by their HCF.

Adding/subtracting like fractions:

Adding/subtracting unlike fractions: Find LCM of denominators, convert, then add.

Comparing fractions: Cross multiply or convert to common denominator.

Decimal to fraction:

Fraction to decimal: Divide numerator by denominator.

Adding/subtracting decimals: Line up decimal points, then add or subtract.

Memory tip: To add unlike fractions, find the LCM of denominators first. To compare fractions, cross-multiplication is the fastest method.

Point: A location with no size.
Line segment: Definite length, two endpoints.
Ray: One endpoint, extends infinitely in one direction.
Line: No endpoints, extends infinitely in both directions.

Types of angles:
- Acute: $0° < \theta < 90°$
- Right: $\theta = 90°$
- Obtuse: $90° < \theta < 180°$
- Straight: $\theta = 180°$
- Reflex: $180° < \theta < 360°$

Angle sum in a triangle:

Angle sum in a quadrilateral:

**Sum of interior angles of a polygon with $n$ sides:**

Circle terms:
- Radius $r$, Diameter $d = 2r$
- Chord (line segment with endpoints on circle)
- Diameter is the longest chord

Memory tip: The angle sum formula $(n-2) \times 180°$ works for any polygon. Triangle: $(3-2) \times 180° = 180°$. Quadrilateral: $(4-2) \times 180° = 360°$.

Rectangle (length $l$, breadth $b$):

Square (side $a$):

Triangle (base $b$, height $h$):

Perimeter of a triangle: Sum of all three sides.

Circle (radius $r$):

Memory tip: Perimeter is always a length (measured in cm, m, etc.). Area is always in square units (cm$^2$, m$^2$, etc.). Never mix them up.

Ratio: A comparison of two quantities of the same unit.

Always express in simplest form by dividing by HCF.
Example: $12 : 18 = 2 : 3$ (divide both by $6$).

Equivalent ratios: Multiply or divide both terms by the same number.

Proportion: Four numbers $a, b, c, d$ are in proportion if:

The numbers $a$ and $d$ are called extremes, and $b$ and $c$ are called means.

Product of extremes = Product of means:

Unitary method: Find the value of one unit, then multiply for the required number of units.

Example: If $5$ pens cost Rs. $30$, what do $8$ pens cost?
Cost of $1$ pen $= \frac{30}{5} = 6$
Cost of $8$ pens $= 6 \times 8 = 48$

Memory tip: In a proportion $a : b :: c : d$, cross-multiply to check: $a \times d$ should equal $b \times c$.

Line of symmetry: A line that divides a figure into two identical halves that are mirror images of each other.

Lines of symmetry in common shapes:

General rule: A regular polygon with $n$ sides has $n$ lines of symmetry.

Memory tip: The more symmetric a shape is, the more lines of symmetry it has. A circle is the most symmetric shape (infinite lines).