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Top Mathematics Formulas

Important mathematics formulas for competitive exams.

1
Percentage Formula
Percentage = (Part / Total) × 100

Calculate the percentage of a given quantity.

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2
Percentage of a Number
Value = (Percentage × Number) / 100

Find a specified percentage of a number.

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3
Percentage Increase
Percentage Increase = ((New Value - Original Value) / Original Value) × 100

Calculate the percentage increase in a value.

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4
Percentage Decrease
Percentage Decrease = ((Original Value - New Value) / Original Value) × 100

Calculate the percentage decrease in a value.

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5
Successive Percentage Changes
Net Change% = A + B + (A × B / 100)

Calculate the net effect of two successive percentage changes.

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6
Profit and Loss
Profit = SP - CP; Loss = CP - SP; Profit% = (Profit / CP) × 100

Calculate profit, loss and profit percentage.

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7
Simple Interest
SI = (P × R × T) / 100

Calculate simple interest on a principal amount.

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8
Speed, Distance and Time
Speed = Distance / Time; Distance = Speed × Time; Time = Distance / Speed

Solve basic motion problems.

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9
Compound Interest
A = P(1 + R/100)^T; CI = A - P

Calculate compound interest compounded annually.

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10
Combined Work
Combined Rate = 1/A + 1/B; Time = 1 / Combined Rate

Find the time required when two workers work together.

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11
Quadratic Equation
x = [-b ± √(b² - 4ac)] / (2a)

Find the roots of a quadratic equation.

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12
Pythagorean Theorem
c² = a² + b²

Calculate the hypotenuse of a right-angled triangle.

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13
Area of a Circle
Area = πr²; Circumference = 2πr

Calculate a circle area and circumference.

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14
Sum of First n Natural Numbers
S = n(n + 1) / 2

Calculate the sum of the first n positive integers.

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15
Difference of Two Squares
a² - b² = (a - b)(a + b)

Factorize a difference of two squares.

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16
Heron Formula
Area = √[s(s-a)(s-b)(s-c)]; s = (a+b+c)/2

Calculate triangle area from all three side lengths.

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17
Basic Sine Ratio
sin θ = Perpendicular / Hypotenuse

Calculate the sine of an acute angle in a right triangle.

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18
Linear Equation in One Variable
ax + b = 0 → x = -b/a

Solve a linear equation with one variable.

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19
Product of Roots of Quadratic
αβ = c/a

Find the product of roots of a quadratic equation.

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20
Remainder Theorem
Remainder = f(a) when f(x) is divided by (x - a)

Find remainder without performing division.

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21
Successive Discounts
Net Discount % = A + B - (A × B)/100

Calculate the equivalent single discount of two successive discounts.

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22
Marked Price Formula
MP = CP × (100 + Profit%) / (100 - Discount%)

Find marked price when cost price, profit and discount are given.

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23
Cost Price from Selling Price
CP = SP × 100 / (100 + Profit%)

Find cost price when selling price and profit percentage are known.

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24
Compound Interest Half Yearly
A = P(1 + R/200)^{2T}

Calculate compound interest when compounded half-yearly.

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25
CI and SI Difference (2 Years)
CI - SI = P(R/100)²

Find the difference between compound and simple interest for 2 years.

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26
Partnership Profit Share
Profit Share ∝ Capital × Time

Distribute profit among partners according to investment and time.

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27
Relative Speed Same Direction
Relative Speed = |u - v|

Find relative speed when two objects move in the same direction.

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28
Relative Speed Opposite Direction
Relative Speed = u + v

Find relative speed when two objects move towards each other.

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29
Downstream Speed
Downstream Speed = u + v

Find speed of boat in the direction of the current.

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30
Upstream Speed
Upstream Speed = u - v

Find speed of boat against the current.

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31
Train Crossing a Pole
Time = Length of Train / Speed of Train

Calculate time taken by a train to cross a pole or a person.

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32
Train Crossing a Platform
Time = (Length of Train + Length of Platform) / Speed

Calculate time taken by a train to cross a platform or bridge.

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33
Work Rate
Work Rate = 1 / Time Taken

Express the portion of work done in one unit of time.

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34
Pipes and Cisterns Filling
Combined Rate = 1/A + 1/B

Find the rate at which two inlet pipes fill a tank together.

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35
Weighted Average
Weighted Average = (n₁x₁ + n₂x₂) / (n₁ + n₂)

Calculate average when different groups have different sizes.

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36
Alligation Rule
(Cheap Qty) : (Dear Qty) = (Dear Price - Mean Price) : (Mean Price - Cheap Price)

Find the ratio in which two ingredients should be mixed.

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37
Area of Triangle
Area = ½ × base × height

Calculate area of a triangle when base and height are known.

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38
Area of Equilateral Triangle
Area = (√3 / 4) × side²

Calculate area of an equilateral triangle from its side.

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39
Area of Rhombus
Area = ½ × d₁ × d₂

Calculate area of a rhombus using its diagonals.

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40
Surface Area of Cuboid
Total Surface Area = 2(lb + bh + hl)

Calculate total surface area of a cuboid.

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41
Volume of Cuboid
Volume = l × b × h

Calculate volume of a cuboid.

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42
Surface Area of Cube
Total Surface Area = 6a²

Calculate total surface area of a cube.

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43
Surface Area of Sphere
Surface Area = 4πr²

Calculate surface area of a sphere.

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44
Volume of Sphere
Volume = (4/3)πr³

Calculate volume of a sphere.

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45
Volume of Cone
Volume = (1/3)πr²h

Calculate volume of a right circular cone.

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46
Diagonal of Cuboid
Diagonal = √(l² + b² + h²)

Find the space diagonal of a cuboid.

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47
Cosine Ratio
cos θ = Adjacent / Hypotenuse

Define cosine of an acute angle in a right triangle.

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48
Tangent Ratio
tan θ = Opposite / Adjacent

Define tangent of an acute angle in a right triangle.

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49
Fundamental Trigonometric Identity
sin²θ + cos²θ = 1

The most important Pythagorean identity.

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50
Complementary Angle Sine
sin(90° - θ) = cos θ

Sine of the complementary angle equals cosine.

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