Mathematical & Financial Formula Hub

$$\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$$

Arithmetic Mean (Average) Formula

The arithmetic mean formula calculates the central average value of a sample dataset by summing all observation values and dividing by the total sample count.

$$\text{Attendance \%} = \left( \frac{N_{\text{attended}}}{N_{\text{total}}} \right) \times 100$$

Attendance Percentage Formula

The attendance percentage formula calculates the proportion of classes attended out of total classes conducted. To maintain a required target criteria (such as 75%), bunk guidance calculates maximum skippable lectures $B = \lfloor \frac{N_{\text{attended}} - T \times N_{\text{total}}}{T} \rfloor$, while recovery guidance calculates required consecutive lectures $R = \lceil \frac{T \times N_{\text{total}} - N_{\text{attended}}}{1 - T} \rceil$.

$$\text{Percentage (\%)} = \text{CGPA} \times 9.5$$

CGPA to Percentage Formula

The CGPA to Percentage conversion formula calculates equivalent percentage marks from CGPA scores for CBSE (CGPA × 9.5), AICTE/VTU ((CGPA - 0.75) × 10), and Mumbai University.

2 variables

$$CPS = \frac{\text{Total Clicks}}{\text{Duration (seconds)}}$$

Clicks Per Second (CPS) Formula

The Clicks Per Second (CPS) formula measures finger tapping frequency over a fixed time interval. It evaluates click speed, finger stamina, and mouse control. CPS is a standard metric used in competitive gaming (such as Minecraft PvP, FPS games, and rhythm titles) and speed testing to benchmark player reflexes.

$$\text{GPA} = \frac{\sum (\text{Course Credit Hours} \times \text{Grade Point Value})}{\sum \text{Course Credit Hours}}$$

Cumulative Grade Point Average (GPA) Formula

Grade Point Average (GPA) standardizes academic performance by weighting earned letter grades against total course credit hours on a standard 4.0 scale.

2 variables

$$\frac{a}{b} \pm \frac{c}{d} = \frac{ad \pm bc}{bd}, \quad \frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}, \quad \frac{a}{b} \div \frac{c}{d} = \frac{ad}{bc}$$

Fraction Calculation Formulas

Fraction arithmetic rules govern addition, subtraction, multiplication, and division of rational numbers by finding common denominators or multiplying numerators and denominators directly.

2 variables

$$\text{GPA} = \frac{\sum (\text{Grade Points}_i \times \text{Credit Hours}_i)}{\sum \text{Credit Hours}_i}$$

GPA Formula (Grade Point Average)

Grade Point Average (GPA) is a weighted average calculation that measures academic performance by multiplying each course grade point value by its credit weight, summing the total quality points, and dividing by total credit hours attempted.

$$\text{LCM}(a, b) \times \text{HCF}(a, b) = a \times b \quad \implies \quad \text{LCM}(a, b) = \frac{a \times b}{\text{HCF}(a, b)}$$

LCM & HCF (GCD) Formula

The Least Common Multiple (LCM) is the smallest positive integer divisible by all numbers in a set, while the Highest Common Factor (HCF or GCD) is the largest integer that divides all numbers without a remainder. For any two positive integers, the product of their LCM and HCF equals the product of the numbers.

$$\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}, \quad \text{Median} = x_{\left(\frac{n+1}{2}\right)}$$

Mean, Median, Mode & Range Formula

Central tendency formulas calculate the arithmetic average (Mean), middle ranking value (Median), most repeated entry (Mode), and total statistical spread (Range) for a numerical dataset.

6 variables

$$\text{Median} = \begin{cases} x_{\left(\frac{n+1}{2}\right)} & \text{if } n \text{ is odd} \[8pt] \frac{x_{\left(\frac{n}{2}\right)} + x_{\left(\frac{n}{2}+1\right)}}{2} & \text{if } n \text{ is even} \end{cases}$$

Median (Middle Value) Formula

The median formula finds the central midpoint value of an ordered numerical sequence, separating the top 50% from bottom 50%.