Power of 10 Calculator — 10ⁿ
Calculate 10ⁿ for any integer or decimal exponent. See the result, scientific notation, SI prefix, number of digits, and a full reference table from 10⁻¹² to 10¹².
Power of 2 Calculator — 2ⁿ
Calculate 2ⁿ for any exponent. See the result, binary representation, nearest power, storage-unit context (KB, MB, GB), and a full reference table from 2⁰ to 2⁶⁴.
2ⁿ Result⧉
1,024.00
2^10
Scientific Notation⧉
≈ 1.0240 × 10^3
Approximate decimal representation
Number of Digits⧉
4.00
Decimal digit count
Binary Representation⧉
10000000000
In binary, 2ⁿ is always 1 followed by n zeros
Storage Context⧉
Exactly 1 KiB
Equivalent in binary storage units (KiB, MiB, GiB…)
CS Application⧉
1 KiB
Common computer-science usage at this bit width
Storage Unit Breakdown
| Unit | Exponent | Relative |
|---|---|---|
| B | 2^0 | |
| KiB | 2^10 | |
| MiB | 2^20 | |
| GiB | 2^30 | |
| TiB | 2^40 | |
| PiB | 2^50 | |
| EiB | 2^60 |
Powers of 2 Reference Table
| n | 2ⁿ | Digits | CS Context | Scale |
|---|---|---|---|---|
| 0 | 1.00 | 1 | — | |
| 1 | 2.00 | 1 | Bit values (0–1) | |
| 2 | 4.00 | 1 | — | |
| 3 | 8.00 | 1 | — | |
| 4 | 16.00 | 2 | Nibble (16 values) | |
| 5 | 32.00 | 2 | — | |
| 6 | 64.00 | 2 | — | |
| 7 | 128.00 | 3 | ASCII characters (128) | |
| 8 | 256.00 | 3 | Byte / uint8 (256 values) | |
| 9 | 512.00 | 3 | — | |
| 10 | 1,024.00 | 4 | 1 KiB | |
| 11 | 2,048.00 | 4 | — | |
| 12 | 4,096.00 | 4 | 4 KiB (memory page) | |
| 13 | 8,192.00 | 4 | — | |
| 14 | 16,384.00 | 5 | — | |
| 15 | 32,768.00 | 5 | — | |
| 16 | 65,536.00 | 5 | uint16 (65,536 values) | |
| 17 | 131,072.00 | 6 | — | |
| 18 | 262,144.00 | 6 | — | |
| 19 | 524,288.00 | 6 | — | |
| 20 | 1,048,576.00 | 7 | 1 MiB | |
| 21 | 2,097,152.00 | 7 | — | |
| 22 | 4,194,304.00 | 7 | — | |
| 23 | 8,388,608.00 | 7 | — | |
| 24 | 16,777,216.00 | 8 | RGB color (16.7M colors) | |
| 25 | 33,554,432.00 | 8 | — | |
| 26 | 67,108,864.00 | 8 | — | |
| 27 | 134,217,728.00 | 9 | — | |
| 28 | 268,435,456.00 | 9 | — | |
| 29 | 536,870,912.00 | 9 | — | |
| 30 | 1,073,741,824.00 | 10 | 1 GiB | |
| 31 | 2,147,483,648.00 | 10 | — | |
| 32 | 4,294,967,296.00 | 10 | uint32 / IPv4 addresses | |
| 33 | 8,589,934,592.00 | 10 | — | |
| 34 | 17,179,869,184.00 | 11 | — | |
| 35 | 34,359,738,368.00 | 11 | — | |
| 36 | 68,719,476,736.00 | 11 | — | |
| 37 | 137,438,953,472.00 | 12 | — | |
| 38 | 274,877,906,944.00 | 12 | — | |
| 39 | 549,755,813,888.00 | 12 | — | |
| 40 | 1,099,511,627,776.00 | 13 | 1 TiB | |
| 41 | 2,199,023,255,552.00 | 13 | — | |
| 42 | 4,398,046,511,104.00 | 13 | — | |
| 43 | 8,796,093,022,208.00 | 13 | — | |
| 44 | 17,592,186,044,416.00 | 14 | — | |
| 45 | 35,184,372,088,832.00 | 14 | — | |
| 46 | 70,368,744,177,664.00 | 14 | — | |
| 47 | 140,737,488,355,328.00 | 15 | — | |
| 48 | 281,474,976,710,656.00 | 15 | MAC addresses | |
| 49 | 562,949,953,421,312.00 | 15 | — | |
| 50 | 1,125,899,906,842,624.00 | 16 | 1 PiB | |
| 51 | 2,251,799,813,685,248.00 | 16 | — | |
| 52 | 4,503,599,627,370,496.00 | 16 | — | |
| 53 | 9,007,199,254,740,992.00 | 16 | JS safe integer limit | |
| 54 | 18,014,398,509,481,984.00 | 17 | — | |
| 55 | 36,028,797,018,963,970.00 | 17 | — | |
| 56 | 72,057,594,037,927,940.00 | 17 | DES key space | |
| 57 | 144,115,188,075,855,870.00 | 18 | — | |
| 58 | 288,230,376,151,711,740.00 | 18 | — | |
| 59 | 576,460,752,303,423,500.00 | 18 | — | |
| 60 | 1,152,921,504,606,847,000.00 | 19 | 1 EiB | |
| 61 | 2,305,843,009,213,694,000.00 | 19 | — | |
| 62 | 4,611,686,018,427,388,000.00 | 19 | — | |
| 63 | 9,223,372,036,854,776,000.00 | 19 | — | |
| 64 | 18,446,744,073,709,552,000.00 | 20 | uint64 / 64-bit address space |
Planning notes, formulas, and examples
About the Power of 2 Calculator — 2ⁿ
Powers of 2 are fundamental in computer science, digital electronics, and information theory. Every byte of data you store, every pixel on your screen, and every address in memory ties back to a power of 2. When a programmer says "a 32-bit integer can hold values up to about 4 billion," they mean 2³² = 4,294,967,296. When your phone has 128 GB of storage, that is 128 × 2³⁰ bytes. This Power of 2 Calculator lets you enter any exponent n and see the exact value of 2ⁿ, its binary representation (a 1 followed by n zeros), the nearest power of 2, and a practical context — which storage unit (KB, MB, GB, TB) the value corresponds to. A comprehensive reference table lists every power from 2⁰ to 2⁶⁴ with the decimal value and common CS usage (byte widths, address spaces, hash sizes). Storage-unit bars visualize how each power maps to familiar units. Eight presets cover the most-used values (8-bit, 16-bit, 32-bit, 64-bit, and memory milestones) so you can compare them directly. Whether you are a student learning binary, a developer sizing data structures, or a hardware engineer choosing address widths, the page keeps the numeric result and the computing context aligned.
When This Page Helps
Powers of 2 are often used as both raw numbers and computing landmarks. You may want the exact integer value, but you may also need to know how it maps to bit width, address space, or storage size. This calculator keeps those views together so the exponent stays connected to its practical meaning.
It is especially useful when you are comparing neighboring powers. Seeing the decimal value, binary pattern, and storage-unit interpretation side by side makes it easier to understand why one extra bit doubles capacity.
How to Use the Inputs
- Enter Exponent n and Table min exponent in the input fields.
- Select the mode, method, or precision options that match your power of 2 calculator — 2ⁿ problem.
- Read 2ⁿ Result first, then use Scientific Notation to confirm your setup is correct.
- Try a preset such as "2⁸ (byte)" to test a known case quickly.
Formula used
2ⁿ. In binary, 2ⁿ is 1 followed by n zeros. Storage: 2¹⁰ = 1 KiB, 2²⁰ = 1 MiB, 2³⁰ = 1 GiB, 2⁴⁰ = 1 TiB.Example Calculation
Result: 2ⁿ Result shown by the calculator
Using the preset "2⁸ (byte)", the calculator evaluates the power of 2 calculator — 2ⁿ setup, applies the selected algebra rules, and reports 2ⁿ Result with supporting checks so you can verify each transformation.
Tips & Best Practices
- 2¹⁰ ≈ 10³ — this is why 1 KB is approximately 1,000 bytes but exactly 1,024.
- The number of values an n-bit unsigned integer can represent is exactly 2ⁿ (from 0 to 2ⁿ − 1).
- To check if a number is a power of 2, use the bit trick: n & (n − 1) === 0.
- Doubling is the same as left-shifting by 1 bit: x << 1 === x × 2.
How This Power of 2 Calculator Works
The calculator raises 2 to the selected exponent, then derives the related views that are most useful in binary and computing contexts: decimal value, scientific notation, digit count, binary representation, nearest power, and storage-size interpretation.
Interpreting Results
Start with the exact value of 2ⁿ, then compare the binary form and the storage or bit-width context. Those supporting outputs make it easier to connect an abstract exponent to a familiar computing scale.
Study Strategy
Compare 2⁸, 2¹⁶, 2³², and 2⁶⁴ in sequence. That progression is a good way to build intuition for how doubling by one bit changes capacity, range, and address-space size.
Sources & Methodology
Last updated:
Frequently Asked Questions
A power of 2 is the result of multiplying 2 by itself n times. For example, 2⁵ = 2 × 2 × 2 × 2 × 2 = 32.
Computers operate in binary (base 2). Memory addresses, data widths, hash sizes, and storage capacities are all built around powers of 2.
KB (kilobyte) often means 1,000 bytes in SI, while KiB (kibibyte) means exactly 1,024 (2¹⁰) bytes. The IEC binary prefixes (KiB, MiB, GiB) avoid ambiguity.
An unsigned n-bit integer can represent 2ⁿ distinct values (0 through 2ⁿ − 1). A signed n-bit integer using two's complement ranges from −2ⁿ⁻¹ to 2ⁿ⁻¹ − 1.
2⁶⁴ = 18,446,744,073,709,551,616 — roughly 18.4 quintillion. This is the size of the 64-bit address space and the maximum value of an unsigned 64-bit integer + 1.
Divide or multiply by 1,024 (2¹⁰) to move one step: bytes → KiB → MiB → GiB → TiB → PiB → EiB.
More in this topic
Power Function Calculator — f(x) = axⁿ
Explore power functions f(x) = axⁿ: compute values, analyze domain, range, symmetry, end behavior, and growth rate. Compare powers with a table and growth bars.
Power Modulo Calculator — aⁿ mod m
Compute aⁿ mod m using modular exponentiation. See the result, step-by-step binary exponentiation, repeated squaring table, and binary decomposition of the exponent.