Calculator Glossary

A

5 terms

Acceleration: The rate of change of velocity over time, measured in meters per second squared (m/s²). Calculated as the change in velocity divided by the time interval. A key concept in physics and engineering.
Amortization: The process of spreading out a loan into a series of fixed payments over time. Each payment covers both interest and principal, with the interest portion decreasing as the principal balance is reduced.
APR (Annual Percentage Rate): The annual rate charged for borrowing or earned through an investment, expressed as a percentage. APR includes fees and additional costs associated with the loan, making it a more complete measure than the simple interest rate.
Aspect Ratio: The proportional relationship between the width and height of an image or display, expressed as two numbers separated by a colon (e.g., 16:9). Common aspect ratios include 4:3 (standard), 16:9 (widescreen), and 21:9 (ultrawide).
Average (Mean): The sum of all values in a dataset divided by the number of values. The arithmetic mean is the most commonly used type of average and provides a central tendency measure for the data.

B

4 terms

BMI (Body Mass Index): A measure of body fat based on height and weight. Calculated as weight in kilograms divided by height in meters squared (kg/m²). Categories: underweight (<18.5), normal (18.5–24.9), overweight (25–29.9), obese (≥30).
BMR (Basal Metabolic Rate): The number of calories your body needs to maintain basic life-sustaining functions at rest, such as breathing, circulation, and cell production. BMR accounts for about 60–75% of daily calorie expenditure.
Body Fat Percentage: The proportion of your total body mass that is fat tissue. Essential fat is 2–5% for men and 10–13% for women. Athletes typically have 6–13% (men) or 14–20% (women). Measured via calipers, bioimpedance, or DEXA scans.
Base (Number Systems): The number of unique digits used in a positional numeral system. Common bases include binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16). Each position represents a power of the base.

C

5 terms

Calorie: A unit of energy. In nutrition, "calorie" typically refers to a kilocalorie (kcal), the energy needed to raise the temperature of 1 kilogram of water by 1 degree Celsius. Used to measure energy content in food and energy expenditure in exercise.
Compound Interest: Interest calculated on both the initial principal and the accumulated interest from previous periods. The formula is A = P(1 + r/n)^(nt), where P is principal, r is annual rate, n is compounding frequency, and t is time in years.
Conversion Factor: A numerical ratio used to convert a measurement from one unit to another. For example, 1 inch = 2.54 centimeters, so the conversion factor from inches to centimeters is 2.54.
Credit Hour: A unit of measurement for college coursework, typically representing one hour of classroom instruction per week over a semester. Most courses are 3 credit hours. Used to calculate GPA and track degree completion.
Circumference: The distance around the edge of a circle. Calculated as C = 2πr or C = πd, where r is the radius and d is the diameter. A fundamental measurement in geometry.

D

3 terms

Density: Mass per unit volume of a substance, typically expressed in kg/m³ or g/cm³. Calculated as ρ = m/V. Water has a density of 1 g/cm³ at 4°C. Used to identify materials and calculate buoyancy.
Down Payment: An initial upfront payment made when purchasing an expensive item on credit, such as a home or car. Typically expressed as a percentage of the total purchase price. A common mortgage down payment is 20%.
Dividend: In division, the number being divided. In finance, a distribution of a company's earnings to its shareholders, usually paid quarterly. Dividend yield is calculated as annual dividends per share divided by the stock price.

E

2 terms

Exponent: A number that indicates how many times a base number is multiplied by itself. In the expression 2³ = 8, the exponent is 3. Also known as a power. Negative exponents represent reciprocals (2&sup-;³ = 1/8).
Equation: A mathematical statement that asserts the equality of two expressions, connected by an equals sign (=). Solving an equation means finding the values of unknowns that make the equation true.

F

3 terms

Factorial: The product of all positive integers less than or equal to a given number, denoted by n!. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. By convention, 0! = 1. Used extensively in combinatorics and probability.
Force: An interaction that changes the motion of an object. Measured in newtons (N). Newton's second law states F = ma (force equals mass times acceleration). Common forces include gravity, friction, and tension.
Frequency: The number of occurrences of a repeating event per unit of time. In physics, measured in hertz (Hz), where 1 Hz equals one cycle per second. Related to wavelength by the equation v = fλ, where v is wave speed.

G

3 terms

GCD (Greatest Common Divisor): The largest positive integer that divides two or more integers without a remainder. Also called Greatest Common Factor (GCF). For example, GCD(12, 18) = 6. Commonly found using the Euclidean algorithm.
GPA (Grade Point Average): A standardized measure of academic achievement calculated by dividing total grade points earned by total credit hours attempted. The 4.0 scale assigns A=4.0, B=3.0, C=2.0, D=1.0, F=0. Weighted GPA may use a 5.0 scale for honors/AP courses.
Gross Pay: Total earnings before any deductions such as taxes, insurance, or retirement contributions. Includes base salary, overtime, bonuses, and commissions. The starting point for calculating net (take-home) pay.

H

2 terms

Heart Rate Zone: Ranges of heart rate intensity used to target specific fitness goals during exercise. Typically divided into 5 zones based on percentage of maximum heart rate: Zone 1 (50–60%, recovery), Zone 2 (60–70%, fat burn), Zone 3 (70–80%, aerobic), Zone 4 (80–90%, anaerobic), Zone 5 (90–100%, VO2 max).
Hypotenuse: The longest side of a right triangle, opposite the right angle. Its length is calculated using the Pythagorean theorem: c = √(a² + b²), where a and b are the other two sides.

I

3 terms

Imperial System: A system of measurement used primarily in the United States and a few other countries. Uses units like inches, feet, miles (length), pounds, ounces (weight), and Fahrenheit (temperature). Contrast with the metric system.
Interest Rate: The proportion of a loan charged as interest to the borrower, typically expressed as an annual percentage. Can be fixed (stays the same) or variable (changes with market conditions). Different from APR, which includes additional fees.
Interpolation: A method of estimating unknown values that fall between known data points. Linear interpolation assumes a straight line between two points. Used in statistics, engineering, and computer graphics.

K

2 terms

Kinetic Energy: The energy an object possesses due to its motion. Calculated as KE = ½mv², where m is mass and v is velocity. Measured in joules (J). Doubling the velocity quadruples the kinetic energy.
Kelvin: The SI base unit of temperature. Zero kelvin (0 K) is absolute zero, the lowest possible temperature. To convert: K = °C + 273.15. There are no negative values on the Kelvin scale.

L

3 terms

LCM (Least Common Multiple): The smallest positive integer that is divisible by two or more integers. For example, LCM(4, 6) = 12. Related to GCD by the formula: LCM(a, b) = |a × b| / GCD(a, b). Used when adding fractions with different denominators.
Logarithm: The inverse operation of exponentiation. log_b(x) = y means b^y = x. Common logarithm uses base 10 (log), natural logarithm uses base e ≈ 2.718 (ln). Used in science, engineering, and to measure earthquake intensity (Richter scale) and sound levels (decibels).
Linear Equation: An equation of the first degree, meaning the variable(s) have an exponent of 1. The standard form is y = mx + b, where m is the slope and b is the y-intercept. Its graph is a straight line.

M

7 terms

Macro (Macronutrient): One of three essential nutrients required in large amounts: protein (4 cal/g), carbohydrates (4 cal/g), and fat (9 cal/g). Tracking macros involves calculating the grams of each consumed daily to meet specific nutritional goals.
Mean: A measure of central tendency. The arithmetic mean is the sum of values divided by the count. Other types include geometric mean (nth root of the product) and harmonic mean (reciprocal of the arithmetic mean of reciprocals).
Median: The middle value in a sorted dataset. If the dataset has an even number of values, the median is the average of the two middle values. Less affected by outliers than the mean, making it useful for skewed distributions.
Metric System: An international decimal system of measurement based on powers of 10. Uses meters (length), grams (mass), liters (volume), and Celsius (temperature). Prefixes include kilo (1000), centi (0.01), and milli (0.001).
Mode: The value that appears most frequently in a dataset. A dataset can have no mode (all values unique), one mode (unimodal), two modes (bimodal), or multiple modes (multimodal). Useful for categorical data.
Molar Mass: The mass of one mole of a substance, expressed in grams per mole (g/mol). Calculated by summing the atomic masses of all atoms in a molecule. For example, water (H&sub2;O) has a molar mass of approximately 18.015 g/mol.
Mortgage: A loan used to purchase real estate, where the property itself serves as collateral. Key components include principal, interest rate, term (typically 15 or 30 years), and monthly payment. The payment is calculated using an amortization formula.

N

2 terms

Net Pay: The amount of money an employee takes home after all deductions from gross pay, including federal and state income taxes, Social Security, Medicare, health insurance premiums, and retirement contributions. Also called take-home pay.
Newton: The SI unit of force. One newton is the force needed to accelerate a 1 kilogram mass at 1 meter per second squared. Named after Sir Isaac Newton. Approximately equal to the force of gravity on a small apple (about 100 grams).

O

2 terms

Ohm's Law: A fundamental law in electronics stating that voltage (V) equals current (I) times resistance (R): V = IR. Also expressed as I = V/R and R = V/I. Named after Georg Simon Ohm. Essential for circuit design and analysis.
Order of Operations: The conventional sequence for evaluating mathematical expressions: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). Remembered by the acronym PEMDAS or BODMAS.

P

5 terms

Percentage: A number expressed as a fraction of 100, denoted by the % symbol. To find a percentage: (part/whole) × 100. To find a value from a percentage: (percentage/100) × total. Ubiquitous in finance, statistics, and everyday calculations.
pH: A measure of the acidity or alkalinity of a solution on a scale of 0 to 14. pH 7 is neutral, below 7 is acidic, above 7 is alkaline (basic). Calculated as pH = −log[H+], where [H+] is the hydrogen ion concentration in moles per liter.
PPI (Pixels Per Inch): A measurement of the pixel density of a screen or digital image. Higher PPI means sharper images. Calculated as the diagonal resolution divided by the screen diagonal size. Common values: 72 PPI (web), 300+ PPI (print quality), 400+ PPI (modern smartphones).
Principal: The original sum of money borrowed in a loan or the initial amount invested. Interest is calculated on the principal. In amortization, each payment reduces the principal while also covering interest charges.
Protein: A macronutrient essential for building muscle, repairing tissue, and producing enzymes. Contains 4 calories per gram. Recommended daily intake is typically 0.8 g per kg of body weight for adults, higher for athletes (1.2–2.0 g/kg).

Q

1 term

Quotient: The result of dividing one number by another. In the expression 15 ÷ 3 = 5, the quotient is 5. In division with remainders, the quotient is the integer part of the result.

R

3 terms

Resistance: The opposition to the flow of electric current in a circuit, measured in ohms (Ω). Depends on material, length, cross-sectional area, and temperature of the conductor. Related to voltage and current by Ohm's law: R = V/I.
ROI (Return on Investment): A performance measure used to evaluate the efficiency of an investment. Calculated as ROI = (Net Profit / Cost of Investment) × 100%. A positive ROI means the investment gained value; negative ROI means it lost value.
Rounding: The process of reducing the number of significant digits in a number. Common rules: if the digit to be dropped is less than 5, round down; if 5 or greater, round up. Banker's rounding rounds to the nearest even number when the digit is exactly 5.

S

4 terms

Scientific Notation: A way of expressing very large or very small numbers as a product of a coefficient (between 1 and 10) and a power of 10. For example, 3,000,000 = 3 × 10&sup6; and 0.00045 = 4.5 × 10&sup-;&sup4;. Standard in science and engineering.
Simple Interest: Interest calculated only on the original principal, not on accumulated interest. Formula: I = P × r × t, where P is principal, r is annual rate, and t is time in years. Simpler but less common than compound interest in modern finance.
Square Root: A value that, when multiplied by itself, gives the original number. Denoted by the radical symbol √. For example, √25 = 5 because 5 × 5 = 25. Every positive number has two square roots (positive and negative), but the principal square root is the positive one.
Standard Deviation: A measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates values are close to the mean; high standard deviation indicates values are spread out. Calculated as the square root of the variance.

T

3 terms

TDEE (Total Daily Energy Expenditure): The total number of calories your body burns in a day, including BMR, physical activity, and the thermic effect of food. Calculated by multiplying BMR by an activity factor (1.2 for sedentary to 1.9 for very active). The baseline for weight management.
Temperature Scales: Systems for measuring temperature. Celsius (°C): water freezes at 0°, boils at 100°. Fahrenheit (°F): water freezes at 32°, boils at 212°. Kelvin (K): absolute zero = 0 K. Conversions: °F = (°C × 9/5) + 32; K = °C + 273.15.
Trigonometry: The branch of mathematics dealing with the relationships between the sides and angles of triangles. Key functions: sine (sin), cosine (cos), tangent (tan). The fundamental identity is sin²θ + cos²θ = 1.

V

4 terms

Variance: A measure of how far a set of numbers are spread out from their mean. Calculated as the average of the squared differences from the mean. The square root of variance gives the standard deviation. Used extensively in statistics and probability.
Velocity: The speed of an object in a given direction, measured in meters per second (m/s). Unlike speed (a scalar), velocity is a vector quantity with both magnitude and direction. Average velocity = displacement / time.
Voltage: The electric potential difference between two points, measured in volts (V). Think of it as the "pressure" that pushes electric charge through a circuit. Common sources: household outlet (120V or 240V), car battery (12V), USB (5V).
Volume: The amount of three-dimensional space occupied by an object or enclosed within a container. Common units: liters, cubic meters, gallons, cubic feet. Formulas vary by shape: cube (s³), sphere (4/3πr³), cylinder (πr²h).

W

2 terms

Wavelength: The distance between consecutive identical points on a wave (e.g., crest to crest), measured in meters. Related to frequency by λ = v/f, where v is wave speed and f is frequency. Visible light wavelengths range from about 380 nm (violet) to 700 nm (red).
Weighted Average: An average where each value is multiplied by a weight reflecting its importance before summing and dividing. Formula: (w1×x1 + w2×x2 + ...) / (w1 + w2 + ...). Used in GPA calculation, portfolio returns, and survey analysis.

Calculator Glossary

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