A 32 bit floating point number has 23 + 1 bits of mantissa and an 8 bit exponent (-126 to 127 is used though) so the largest number you can represent is:
(1 + 1 / 2 + ... 1 / (2 ^ 23)) * (2 ^ 127) =
(2 ^ 23 + 2 ^ 23 + .... 1) * (2 ^ (127 - 23)) =
(2 ^ 24 - 1) * (2 ^ 104) ~= 3.4e38
Top answer 1 of 6
32
A 32 bit floating point number has 23 + 1 bits of mantissa and an 8 bit exponent (-126 to 127 is used though) so the largest number you can represent is:
(1 + 1 / 2 + ... 1 / (2 ^ 23)) * (2 ^ 127) =
(2 ^ 23 + 2 ^ 23 + .... 1) * (2 ^ (127 - 23)) =
(2 ^ 24 - 1) * (2 ^ 104) ~= 3.4e38
2 of 6
23
These numbers come from the IEEE-754 standard, which defines the standard representation of floating point numbers. Wikipedia article at the link explains how to arrive at these ranges knowing the number of bits used for the signs, mantissa, and the exponent.
GeeksforGeeks
geeksforgeeks.org › c language › c-float-and-double
C Float and Double - GeeksforGeeks
July 23, 2025 - It can store values up to 7 decimal points without loss of precision. The format specifier for float is %f.
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TutorialsPoint
tutorialspoint.com › cprogramming › c_data_types.htm
C - Data Types
CHAR_BIT : 8 CHAR_MAX : 127 CHAR_MIN : -128 INT_MAX : 2147483647 INT_MIN : -2147483648 LONG_MAX : 9223372036854775807 LONG_MIN : -9223372036854775808 SCHAR_MAX : 127 SCHAR_MIN : -128 SHRT_MAX : 32767 SHRT_MIN : -32768 UCHAR_MAX : 255 UINT_MAX : 4294967295 ULONG_MAX : 18446744073709551615 USHRT_MAX : 65535 · The following table provides the details of standard floating-point types with storage sizes and value ranges and their precision −
Microsoft Learn
learn.microsoft.com › en-us › dotnet › csharp › language-reference › builtin-types › floating-point-numeric-types
Floating-point numeric types - C# reference | Microsoft Learn
January 20, 2026 - Each of the floating-point types has the MinValue and MaxValue constants that provide the minimum and maximum finite value of that type. The float and double types also provide constants that represent not-a-number and infinity values.
Codefinity
codefinity.com › blog › Float-vs-Double
Float vs Double
The primary difference between float and double is the precision. Float is a single-precision float with about 7 decimal digits of precision and a range from approximately 1.4E-45 to 3.4E+38.
Wikipedia
en.wikipedia.org › wiki › C_data_types
C data types - Wikipedia
1 week ago - The C language provides the four basic arithmetic type specifiers char, int, float and double (as well as the Boolean type bool), and the modifiers signed, unsigned, short, and long. The following table lists the permissible combinations in specifying a large set of storage size-specific declarations. ^ The standard term for the size of an integer type in bits is width. The width does not include padding bits. ^ a b c d e The minimal ranges [−(2n−1−1), 2n−1−1] (e.g.
W3Resource
w3resource.com › c-programming › c-data-types.php
C Data Types - w3resource
August 19, 2022 - Ranges for integer data types in ...------------------------------------- flaot 1.175494e-38 3.402823e+38 double 2.225074e-308 1.797693e+308 long double 3.362103e-4932 1.189731e+4932...
Quora
quora.com › How-do-we-find-the-range-of-a-float-in-C
How do we find the range of a float in C++? - Quora
Answer (1 of 2): This isn’t really ... And these IEEE rules define the minimum and maximum values of a float to be minus infinity and plus infinity respectively. What do......
Microsoft Learn
learn.microsoft.com › en-us › cpp › c-language › type-float
Type float | Microsoft Learn
The mantissa represents a number between 1.0 and 2.0. Since the high-order bit of the mantissa is always 1, it is not stored in the number. This representation gives a range of approximately 3.4E-38 to 3.4E+38 for type float.
Quora
quora.com › What-are-the-exact-minimum-and-maximum-range-of-float-double-and-long-double-data-type-in-C
What are the exact minimum and maximum range of float, double, and long double data type in C? - Quora
Answer (1 of 3): > What are the exact minimum and maximum range of float, double, and long double data type in C? The ranges can vary from one implementation to another. The ISO C standard imposes minimal values for the bounds of the floating-point types (and the integer types), but implementati...
GeeksforGeeks
geeksforgeeks.org › c language › data-types-in-c
Data Types in C - GeeksforGeeks
Size: typically 4 bytes, Range: -2,147,483,648 to 2,147,483,647. Format specifier: %d. Format specifiers are the symbols that are used for printing and scanning values of given data types.
Published 3 weeks ago
W3Schools
w3schools.com › c › ref_keyword_float.php
C float Keyword
C Examples C Real-Life Examples C Exercises C Quiz C Code Challenges C Compiler C Syllabus C Study Plan C Interview Q&A C Certificate ... The float keyword is a data type which stores fractional numbers.
IBM
ibm.com › docs › en › informix-servers › 14.10.0
FLOAT(n)
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Scaler
scaler.com › home › topics › what is float in c++?
What is Float in C++? - Scaler Topics
June 19, 2024 - The float in C++ has a precision only up to the 7 digits, if we exceed its precision limit then it displays the garbage values after the precision limit. The range of float type in the C++ can represents values ranging from approximately
Arduino
arduino.cc › en › Reference › float
float | Arduino Documentation
Arduino programming language can be divided in three main parts: functions, values (variables and constants), and structure.
Reddit
reddit.com › r/learnprogramming › float vs double (c++)
r/learnprogramming on Reddit: float vs double (C++)
June 1, 2021 -
I am taking my first programming class, and I have done a few assignments, but I’m not clear on when to use float and when to use double? I know that float uses 4 bits and double uses 8 bits but Im just not sure about what situations call for which. (sorry if this is the wrong community for this question)
Top answer 1 of 3
5
A float is most commonly 32 bits and a double typically 64 bits, not 4 and 8 as you said. When to use which is just a matter of how much precision your need for the things you are calculating, but when in doubt, just use double all the time. The only advantage of using float is that they take up less memory, and unless you have huge arrays of them or are programming on a really tiny platform it probably won't matter.
2 of 3
2
You have to use double when you want to calculate with floating point values with more digits of precision. The usual range of precision possible for floats is between 6 to 9 digits, compared to double's 15 to 18. In calculations that would require more precision you would introduce major floating point calculation errors when using only float type. Errors can also accumulate over many repeated operations where double will give you more leeway. For a lot of use cases float is just enough. float uses 4 bits and double uses 8 bits Typo? Float uses 4 bytes (32 bits), double uses 8 bytes (64 bits.) Also see this toy that can help you visualize how floating point values work on a bit level: https://www.h-schmidt.net/FloatConverter/IEEE754.html
Medium
medium.com › @Dev_Frank › datatypes-in-c-int-char-float-def790690c42
DATATYPES IN C (int, char, float) | by Dev Frank | Medium
February 5, 2024 - The size of a float variable is typically 4 bytes on most systems. It may vary depending on the compiler and platform. The range of a floating number is -3.4e38 to 3.4e38.
W3Schools
w3schools.com › c › c_data_types.php
C Data Types
// Create variables int myNum = 5; // Integer (whole number) float myFloatNum = 5.99; // Floating point number char myLetter = 'D'; // Character // Print variables printf("%d\n", myNum); printf("%f\n", myFloatNum); printf("%c\n", myLetter); Try it Yourself » ·
Wikipedia
en.wikipedia.org › wiki › Floating-point_arithmetic
Floating-point arithmetic - Wikipedia
2 weeks ago - However, the behavior may not be the same as a rounding to the destination format due to a possible wider exponent range of the extended format. A floating-point number consists of two fixed-point components, whose range depends exclusively on the number of bits or digits in their representation.
Top answer 1 of 2
5
$1.2\times 10^{-38}$ is a decimal value. You need to convert it to binary exponential notation to see how the bits are set.
Another small mistake: $2^6+...2^1+2^0$ does not equal $2^{27}$, it equals $2^7-1$.
2 of 2
3
With 7 exponent bits and one sign bit for the exponent (a total of 8 bits), you can express numbers in the range of $2^{-127}\approx 5.9\cdot 10^{-39}$ to $2^{+127} \approx 1.7\cdot 10^{38}$.
But then you multiply these numbers by numbers of the form $1.bbbbbbb...$ in binary notation, where each of the $b$ stands for one of the 23 bits of the mantissa (i.e., each $b$ is either zero or one). This already gives you a nonsymmetric distribution.
But then not all bit combinations are valid anyway. For example, if I recall correctly, an exponent of -127 is not valid and is interpreted as marking the floating point number as some infinity or NaN, and so in reality, the numbers you can then represent are all of the form $$ 1.bbbbbbb... \cdot 2^{-126} \quad\text{to}\quad 1.bbbbbbb... \cdot 2^{+127}. $$