Hexadecimal to Decimal Converter
Instantly convert hexadecimal decimal with our free converter. See conversion tables, formulas, and step-by-step explanations.
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Adjust values & calculatePlace Value Breakdown
| Hex Digit | Decimal Value | 16^pos | Result |
|---|---|---|---|
| F | 15 | 16 | 240 |
| F | 15 | 1 | 15 |
Formula
Hexadecimal uses base 16 with digits 0-9 and A-F (representing 10-15). To convert hex to decimal, each digit is multiplied by 16 raised to its positional power and the results are summed. To convert decimal to hex, repeatedly divide by 16 and map remainders to hex digits.
Last reviewed: December 2025
Worked Examples
Example 1: CSS Color Code Conversion
Example 2: Memory Address Conversion
Background & Theory
The Hexadecimal to Decimal Converter applies the following established principles and formulas. Unit conversion is the process of expressing a quantity in a different unit of measurement while preserving its physical meaning. At the foundation of modern measurement lies the International System of Units (SI), which defines seven base units: the meter for length, kilogram for mass, second for time, ampere for electric current, kelvin for thermodynamic temperature, mole for amount of substance, and candela for luminous intensity. All other units, called derived units, are defined as algebraic combinations of these seven. Dimensional analysis is the principal method for performing unit conversions. By treating units as algebraic quantities that can be multiplied, divided, and cancelled, a conversion factor chain allows a value expressed in one unit to be rewritten in another without altering its physical magnitude. For example, to convert 60 miles per hour to meters per second, one multiplies by a chain of conversion factors each equal to one: (1609.34 m / 1 mile) × (1 hour / 3600 s). Metric prefixes enable compact expression of quantities across extreme ranges of magnitude. Standard prefixes span from nano (10^-9) through micro (10^-6) and milli (10^-3) up through kilo (10^3), mega (10^6), and giga (10^9), and beyond in both directions. These prefixes are strictly multiplicative and apply consistently to any SI base or derived unit. Temperature conversions require affine transformations rather than simple scaling. To convert Celsius to Fahrenheit the formula is °F = (°C × 9/5) + 32, while the conversion to the absolute Kelvin scale is K = °C + 273.15. These formulas reflect the different zero points and degree-size conventions of each scale. Significant figures govern how precision is preserved through calculations. A result should not express more precision than the least precise input value permits. In digital storage, IEEE and IEC standards distinguish between decimal prefixes (kilobyte = 1000 bytes) and binary prefixes (kibibyte = 1024 bytes), a distinction that has practical consequences for how storage capacity is reported by manufacturers versus operating systems. Unit coherence — ensuring that all quantities in an equation share a consistent unit system — is essential for obtaining correct results.
History
The history behind the Hexadecimal to Decimal Converter traces back through the following developments. Human beings have been measuring and comparing quantities since before recorded history. The earliest known measurement units were body-based: the cubit (the distance from elbow to fingertip), the foot, the hand, and the digit. The furlong originated as the length of a furrow a team of oxen could plow without resting. These anthropomorphic standards were practical for local use but differed between regions and kingdoms, creating persistent difficulties in trade and construction. The ancient Egyptians standardized the royal cubit at approximately 52.4 centimeters and distributed calibrated granite rods to ensure consistency across building projects, including the pyramids. Roman engineers used the mile (mille passuum, one thousand double paces) and spread these standards throughout their empire via road networks. Despite these efforts, measurement diversity persisted across medieval Europe, hampering commerce. The French Revolution created political will for radical standardization. In 1795 France officially adopted the metric system, defining the meter as one ten-millionth of the distance from the equator to the North Pole along the Paris meridian. This gave the world its first fully decimal, rationally constructed measurement system. The Metre Convention of 1875 established the International Bureau of Weights and Measures (BIPM) in Sevres, France, creating a permanent international body to maintain physical artifact standards and coordinate global metrology. For over a century, the kilogram was defined by a platinum-iridium cylinder locked in a vault near Paris. In 1999, a stark demonstration of what unit inconsistency costs occurred when NASA's Mars Climate Orbiter was lost because one engineering team used pound-force seconds while another used newton seconds. The spacecraft entered the Martian atmosphere at the wrong angle and was destroyed, at a cost of 327 million dollars. In 2019 the SI underwent its most significant revision, redefining all seven base units in terms of fixed numerical values of fundamental physical constants such as the speed of light, Planck's constant, and the elementary charge. This eliminated any reliance on physical artifacts and made the measurement system permanently stable and universally reproducible.
Frequently Asked Questions
Formula
Decimal = Sum of (hex_digit x 16^position) | Hex = Repeated division by 16
Hexadecimal uses base 16 with digits 0-9 and A-F (representing 10-15). To convert hex to decimal, each digit is multiplied by 16 raised to its positional power and the results are summed. To convert decimal to hex, repeatedly divide by 16 and map remainders to hex digits.
Worked Examples
Example 1: CSS Color Code Conversion
Problem: Convert hex color #3CB371 (medium sea green) to its decimal RGB values.
Solution: Red: 3C hex = 3 x 16 + 12 = 60\nGreen: B3 hex = 11 x 16 + 3 = 179\nBlue: 71 hex = 7 x 16 + 1 = 113
Result: RGB(60, 179, 113)
Example 2: Memory Address Conversion
Problem: Convert the hexadecimal memory address 0x7FFF to decimal.
Solution: 7 x 16^3 = 7 x 4096 = 28672\nF x 16^2 = 15 x 256 = 3840\nF x 16^1 = 15 x 16 = 240\nF x 16^0 = 15 x 1 = 15\nTotal = 28672 + 3840 + 240 + 15
Result: 0x7FFF = 32,767 in decimal
Frequently Asked Questions
Why is hexadecimal used in computing?
Hexadecimal is widely used in computing because it provides a compact, human-readable representation of binary data. Each hex digit maps exactly to four binary digits (bits), making conversions straightforward. This is especially useful for representing memory addresses, color codes in web design (like #FF5733), MAC addresses, and byte values. A single byte (8 bits) can be represented by exactly two hex digits, ranging from 00 to FF.
What do the letters A through F mean in hexadecimal?
In hexadecimal notation, letters A through F represent the values 10 through 15 respectively. Since hexadecimal is base-16, it needs 16 unique symbols. The digits 0 through 9 cover the first ten values, and the letters A (10), B (11), C (12), D (13), E (14), and F (15) complete the set. Both uppercase and lowercase letters are valid and interchangeable in hex notation.
How do you convert decimal to hexadecimal?
To convert decimal to hexadecimal, repeatedly divide the decimal number by 16, recording each remainder. Convert any remainder of 10 or higher to its letter equivalent (10=A, 11=B, 12=C, 13=D, 14=E, 15=F). Continue dividing the quotient by 16 until it reaches zero, then read the hex digits from the last remainder to the first. For example, 255 divided by 16 is 15 remainder 15, then 15 divided by 16 is 0 remainder 15, giving FF in hex.
Is my data stored or sent to a server?
No. All calculations run entirely in your browser using JavaScript. No data you enter is ever transmitted to any server or stored anywhere. Your inputs remain completely private.
What inputs do I need to use Hexadecimal to Decimal Converter accurately?
Each field is labelled with the required unit (metric or imperial). Gather your source values before starting — for example, a weight measurement in kilograms, a distance in metres, or a dollar amount — and enter them exactly as measured. The formula section on this page lists every variable and explains what each represents.
How do I interpret the result?
Results are displayed with a label and unit to help you understand the output. Many calculators include a short explanation or classification below the result (for example, a BMI category or risk level). Refer to the worked examples section on this page for real-world context.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy