What is the time complexity of accessing an element in an array?

The time complexity of accessing an element in an array is O(1) (constant).

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#Why

An array is stored in a contiguous memory area, and each element has a fixed size. To find the element at index i, the processor simply calculates its address using the formula:

[ \text{address} = \text{start_address} + i \times \text{element_size} ]

That is, access requires no traversal or search, just one arithmetic operation and one memory access.

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#What this means

• It doesn't matter how many elements are in the array, 10 or 10 million, the time to get any element is the same.
• That's why operations like arr[i] run in constant time.

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#Important

• O(1) is the ideal case for access.
• But searching by value (for example, "find the number 42 in the array") is already O(n), because every element has to be checked.

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Summary:

Accessing an array element by index runs in O(1), instantly, regardless of the array's size.