Mathematical & Financial Formula Hub

Mathematics & Education

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Arithmetic Mean (Average) Formula

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

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.

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Mathematics & Education

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Attendance Percentage Formula

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

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 $R = \lceil \frac{T \times N_{\text{total}} - N_{\text{attended}}}{1 - T} \rceil$.

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BAC Formula

$$BAC\% = \frac{\text{Alcohol Consumed (g)}}{\text{Body Weight (g)} \times r} \times 100 - (0.015 \times \text{Hours})$$

The Widmark formula estimates Blood Alcohol Concentration by dividing the total grams of alcohol consumed by body weight adjusted for a gender-based body-water distribution constant, then subtracting the amount the body has already metabolized over elapsed time at an average elimination rate. It is widely used to give a rough estimate of impairment level, though it is not a substitute for an actual breathalyzer or blood test.

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BMI Formula

$$BMI = \frac{weight\ (kg)}{height^2\ (m^2)}$$

Body Mass Index (BMI) is a simple, widely used metric to estimate whether a person has a healthy body weight relative to their height. BMI categorizes individuals into underweight (under 18.5), normal weight (18.5 - 24.9), overweight (25 - 29.9), and obese (30 and above). It acts as a screening tool to identify possible weight problems for adults.

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BMR Formula

$$\begin{aligned} \text{BMR (Men)} &= 10 \times \text{weight (kg)} + 6.25 \times \text{height (cm)} - 5 \times \text{age (y)} + 5 \\ \text{BMR (Women)} &= 10 \times \text{weight (kg)} + 6.25 \times \text{height (cm)} - 5 \times \text{age (y)} - 161 \end{aligned}$$

Basal Metabolic Rate (BMR) represents the minimum number of calories your body needs to function at rest (e.g. breathing, circulation, cell production, temperature regulation). BMR is estimated using the Mifflin-St Jeor equation, which is widely considered the most accurate standard for calorie planning.

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Body Fat Formula

$$\begin{aligned} \text{Male Body Fat \%} &= \frac{495}{1.0324 - 0.19077\log_{10}(\text{Waist}-\text{Neck}) + 0.15456\log_{10}(\text{Height})} - 450 \\ \text{Female Body Fat \%} &= \frac{495}{1.29579 - 0.35004\log_{10}(\text{Waist}+\text{Hip}-\text{Neck}) + 0.22100\log_{10}(\text{Height})} - 450 \end{aligned}$$

The U.S. Navy Method estimates body fat percentage from simple circumference measurements rather than calipers or DEXA scans, using a regression formula developed by Hodgdon & Beckett that predicts body density from waist, neck, hip (for women), and height, then converts that density to a body fat percentage using the Siri equation (the 495/D − 450 term).

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Body Surface Area Formula

Mosteller Formula — $$BSA = \sqrt{\frac{\text{Height (cm)} \times \text{Weight (kg)}}{3600}}$$

The Mosteller formula is the simplest and most widely used method for estimating Body Surface Area, a measurement used clinically for drug dosing (especially chemotherapy) and for normalizing physiological measurements like kidney filtration rate (eGFR). Several other validated formulas exist (Du Bois, Haycock, Gehan & George, Boyd), each using slightly different regression coefficients, and are often averaged together since no single formula is universally agreed upon as most accurate.

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Finance

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Break-Even Point Formula

$$\text{Break-Even Units} = \frac{\text{Total Fixed Costs}}{\text{Selling Price per Unit} - \text{Variable Cost per Unit}}$$

The break-even point calculates the exact sales volume in units or revenue required to cover total operational expenses, yielding zero net profit and zero net loss.

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Finance

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Break-Even Selling Price Formula

$$\text{Break-Even Price} = \frac{\text{Total Fixed Costs} + \text{Total Variable Costs}}{\text{Expected Number of Units}}$$

The break-even selling price formula calculates the minimum price per unit required to cover all production costs for a target sales volume.

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Built-Up Area Formula

$$\text{Built-Up Area} = \frac{\text{Carpet Area}}{1 - \frac{\text{Wall \& Balcony Share}\%}{100}}$$

Built-Up Area adds the thickness of walls and any balcony space to the Carpet Area, representing a unit's full physical footprint. Since most listings and price quotes reference Built-Up (or Super Built-Up) Area rather than Carpet Area, this formula helps buyers convert between the two to estimate real usable space or verify a quoted built-up figure.

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