Calculator Methodology

Percentage of a number: Result = (Percentage / 100) × Value. Example: 20% of 150 = 0.20 × 150 = 30.

Percentage change: Change = ((New - Original) / Original) × 100. The denominator is always the original value.

Reverse percentage: Original = Final / (1 ± Rate/100). For increase, use +; for decrease, use -.

ROI: ((Final Value - Investment) / Investment) × 100. Does not account for time.

Compound Interest: A = P × (1 + r/n)^(n×t), where P = principal, r = annual rate, n = compounding frequency, t = years.

Loan/Mortgage Payment: M = P × [r(1+r)^n] / [(1+r)^n - 1], where r = monthly rate, n = total months. This covers principal and interest only; it does not include taxes, insurance, or PMI.

Savings Growth: Combines compound interest on the initial amount with the future value of an annuity for monthly deposits.

CAGR (Investment Return): (Final / Initial)^(1/years) - 1. This annualizes the total return.

Profit Margin: ((Revenue - Cost) / Revenue) × 100. Margin is based on revenue.

Markup: ((Price - Cost) / Cost) × 100. Markup is based on cost, not price.

Break-Even: Fixed Costs / (Price - Variable Cost per Unit). This gives the number of units needed to cover all costs.

Revenue Growth: ((Current - Previous) / Previous) × 100. Always divide by the previous period.

VAT (Add): Gross = Net × (1 + VAT Rate / 100).

VAT (Remove): Net = Gross / (1 + VAT Rate / 100). This correctly extracts the net from a VAT-inclusive amount.

Sales Tax: Total = Amount + (Amount × Rate / 100). Simple addition to the purchase amount.

Conversion Rate: (Conversions / Visitors) × 100.

CTR: (Clicks / Impressions) × 100.

CPC: Total Cost / Number of Clicks.

CPM: (Total Cost / Impressions) × 1000. Cost per thousand impressions.

ROAS: Revenue from Ads / Ad Spend. Expressed as a ratio (e.g., 4:1).

Weighted Grade: Each assignment score (earned/total) is multiplied by its weight, and the results are summed. Letter grades follow the standard 90/80/70/60 scale.

GPA: Grade points (4.0 scale) are multiplied by credit hours, summed, and divided by total credits. The standard scale includes +/- grades.

BMI: Metric: weight(kg) / height(m)². Imperial: (weight(lbs) × 703) / height(in)². Categories: under 18.5 = underweight, 18.5-24.9 = normal, 25-29.9 = overweight, 30+ = obese.

Calories (TDEE): Uses the Mifflin-St Jeor equation for BMR, multiplied by an activity factor. BMR (male) = 10×weight(kg) + 6.25×height(cm) - 5×age + 5. BMR (female) = 10×weight(kg) + 6.25×height(cm) - 5×age - 161.

Length & Weight: All conversions go through a base unit (meters for length, grams for weight) to ensure accuracy.

Temperature: Celsius is used as the intermediate unit. °F = °C × 9/5 + 32. K = °C + 273.15.

Currency: Requires a user-supplied exchange rate. We do not provide real-time rates due to constant fluctuation.