Mathematical & Financial Formula Hub

Mathematics & Education

Verified

LCM & HCF (GCD) Formula

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

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.

3 variables

Learn Formula

Health

Verified

Lean Body Mass Formula

$$\begin{aligned} \text{Boer (Male):} \quad &LBM = 0.407W + 0.267H - 19.2 \\ \text{Boer (Female):} \quad &LBM = 0.252W + 0.473H - 48.3 \end{aligned}$$

Lean Body Mass represents everything in the body except fat. The Boer formula estimates it directly from weight and height using gender-specific regression coefficients, without requiring a body fat percentage measurement. It is commonly averaged together with other validated equations (James, Hume formulas) for a more robust estimate, and is useful for tracking muscle mass and setting nutrition targets independent of fat mass changes.

3 variables

Learn Formula

Unit Converters

Verified

Liters to Gallons Formula

$$\text{Gallons (US)} = \text{Liters} \times 0.264172$$

One US liquid gallon equals 3.78541 liters (approx 0.264172 US gallons per liter). An Imperial UK gallon equals 4.54609 liters.

2 variables

Learn Formula

Finance

Verified

Loan Prepayment vs SIP Investment Opportunity Cost Formula

$$\text{Interest Saved} = \sum_{t=1}^{n_{\text{orig}}} I_{\text{orig}}(t) - \sum_{t=1}^{n_{\text{prep}}} I_{\text{prep}}(t)$$ $$\text{SIP Future Wealth} = P_{\text{SIP}} \times \frac{(1 + r_{\text{SIP}})^m - 1}{r_{\text{SIP}}} \times (1 + r_{\text{SIP}})$$ $$\Delta \text{Net Wealth Difference} = \text{SIP Future Wealth} - \text{Total Interest Saved}$$

The Loan Prepayment vs Investment decision is a classic corporate finance and personal wealth dilemma. Prepaying a debt provides a guaranteed, risk-free return equivalent to the effective post-tax loan interest rate (e.g., 8.5%–9.5%). In contrast, investing surplus capital into a diversified Equity SIP targets a higher expected historical return (12%–14%), but carries market volatility risk. This formula quantifies the mathematical wealth difference between total interest saved versus terminal investment compounding.

5 variables

Learn Formula

Finance

Verified

Lumpsum Mutual Fund Formula

$$A = P \times \left(1 + \frac{r}{n}\right)^{n \cdot t}$$

The Lumpsum Mutual Fund Formula calculates the future value of a one-time upfront investment based on compound interest. It models how capital appreciates over time when 100% of the funds compound continuously or periodically.

5 variables

Learn Formula

Health

Verified

Macro Split Formula

$$\text{Protein (g)} = \frac{\text{Calories} \times P\%}{4}, \quad \text{Carbs (g)} = \frac{\text{Calories} \times C\%}{4}, \quad \text{Fat (g)} = \frac{\text{Calories} \times F\%}{9}$$

Once a daily calorie target is set, that budget must be split across the three macronutrients. Each diet archetype allocates a different percentage of calories to protein, carbs, and fat — for example, a ketogenic diet allocates only 5% to carbs and 75% to fat, while a balanced diet spreads more evenly. Converting each macro's calorie share into grams requires dividing by its calories-per-gram value (4 for protein/carbs, 9 for fat, since fat is more energy-dense).

3 variables

Learn Formula

Mathematics & Education

Verified

Mean, Median, Mode & Range Formula

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

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

Learn Formula

Mathematics & Education

Verified

Median (Middle Value) Formula

$$\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}$$

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

3 variables

Learn Formula

Unit Converters

Verified

Miles to Kilometers Formula

$$\text{Kilometers} = \text{Miles} \times 1.609344$$

To convert statute miles to kilometers, multiply the mile value by 1.609344.

2 variables

Learn Formula

Unit Converters

Verified

Milliliters to Fluid Ounces Formula

$$\text{Fluid Ounces (US)} = \text{Milliliters} \times 0.033814$$

One US fluid ounce equals 29.5735 milliliters. To convert milliliters to US fluid ounces, multiply by 0.033814.

2 variables

Learn Formula