Mathematical & Financial Formula Hub

Mathematics & Education

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Statistical Mode Formula

$$\text{Mode} = L + \left[ \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \right] \times h$$

The mode represents the specific value or continuous frequency peak that appears with the highest frequency in a statistical distribution.

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Mathematics & Education

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Statistical Range Formula

$$\text{Range} = x_{\max} - x_{\min}$$

The statistical range formula measures total dispersion by calculating the numerical distance between the highest and lowest values in a distribution.

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Finance

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Sukanya Samriddhi Yojana (SSY) Maturity Formula

$$A = P \times \frac{(1 + r)^n - 1}{r} \times (1 + r)$$

Sukanya Samriddhi Yojana (SSY) compounds interest annually on deposits made for up to 15 years. The account matures after 21 years from account opening, accumulating tax-free returns under Section 80C.

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Real Estate

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Super Built-Up Area Formula

$$\text{Super Built-Up Area} = \text{Built-Up Area} \times \left(1 + \frac{\text{Loading}\%}{100}\right)$$

Super Built-Up Area — often called "saleable area" — is the figure developers actually price and sell against. It adds a "loading" percentage on top of the Built-Up Area to account for the buyer's proportionate share of shared building amenities, so understanding the loading factor helps a buyer see how much of the quoted price is for their own flat versus common spaces.

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Finance

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Swiggy & Zomato Restaurant Net Payout & Profit Formula

$$\text{Net Payout} = (\text{Item Total} + \text{Packaging} - \text{Discount Share}) - \text{Platform Commission} - \text{PG Fee} - \text{GST Deductions} - \text{TCS/TDS}$$ $$\text{Net In-Pocket Profit} = \text{Net Payout} - \text{Food Cost (COGS)} - \text{Allocated Kitchen Overheads}$$

Online food delivery aggregator platforms like Swiggy and Zomato deduct multiple service charges before releasing weekly merchant payouts. These deductions include base platform commissions, 18% GST on aggregator commission and payment gateway fees, Section 194O TDS (1%), Section 52 TCS (0.5%–1%), and customer-funded discount splits. To determine true cloud kitchen or dine-in restaurant delivery profitability, owners must reconcile gross order value against raw material cost of goods sold (COGS) and fixed kitchen operational overheads.

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Finance

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Systematic Withdrawal Plan (SWP) Formula

$$V_{t+1} = (V_t - W) \times (1 + r)$$

A Systematic Withdrawal Plan (SWP) allows mutual fund investors to redeem a fixed amount regularly while remaining capital continues earning market returns.

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Health

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Target Heart Rate Formula

$$\begin{aligned} \text{Tanaka (Max HR)} \quad &MHR = 208 - (0.7 \times \text{age}) \\ \text{Haskell \& Fox (Max HR)} \quad &MHR = 220 - \text{age} \\ \text{Karvonen (Target HR)} \quad &\text{Target HR} = ((MHR - \text{Resting HR}) \times \text{\%Intensity}) + \text{Resting HR} \end{aligned}$$

Calculating a target heart rate training zone actually involves two separate decisions: which formula to use for estimating Maximum Heart Rate (MHR), and then how to convert that MHR into an actual target zone. Haskell & Fox's "220 minus age" is the older, simpler, and most widely recognized MHR formula, but it was derived from a relatively small and non-representative sample. Tanaka's formula (208 − 0.7×age) is a more recent, research-validated alternative developed from a meta-analysis of a much larger dataset, and tends to be considered more accurate, particularly for older adults. Once an MHR estimate is chosen, the Karvonen method converts it into a target heart rate by factoring in resting heart rate (via Heart Rate Reserve) rather than just applying a flat percentage of MHR, which produces more personalized training zones for people with different fitness levels.

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Finance

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Target Net Profit Formula

$$\text{Target Sales Units} = \frac{\text{Total Fixed Costs} + \text{Desired Target Net Profit}}{\text{Selling Price per Unit} - \text{Variable Cost per Unit}}$$

The target net profit formula calculates the total unit sales volume and gross revenue required to achieve a specific profit goal beyond breaking even.

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Health

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TDEE Formula

$$\begin{aligned} BMR &= 10W + 6.25H - 5A + s \\ TDEE &= BMR \times \text{Activity Multiplier} \end{aligned}$$

The Mifflin-St Jeor Equation calculates Basal Metabolic Rate (BMR) — the calories your body burns at complete rest — from weight, height, age, and gender. Multiplying BMR by an activity factor scales it up to Total Daily Energy Expenditure (TDEE), the actual number of calories burned per day including movement and exercise, which is the standard baseline for setting weight loss, maintenance, or gain calorie targets.

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Tax

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TDS Formula

$$\begin{aligned} \text{TDS Amount} &= \text{Payment Amount} \times \frac{\text{TDS Rate}}{100} \\ \text{Net Payable} &= \text{Payment Amount} - \text{TDS Amount} \end{aligned}$$

Tax Deducted at Source (TDS) is a mechanism where the person responsible for making specific payments deducts income tax before releasing the funds to the payee. The tax deducted is credited to the payee's tax account (Form 26AS).

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