Example Data Table
| Virtual Memory | Physical Memory | Page Size | Entry Size | Process Size | Expected Use |
|---|---|---|---|---|---|
| 4 GB | 1 GB | 4 KB | 4 B | 64 MB | Classical paging practice |
| 8 GB | 2 GB | 8 KB | 8 B | 128 MB | Larger entry comparison |
| 16 GB | 4 GB | 16 KB | 8 B | 512 MB | Reduced page count study |
Formula Used
Number of virtual pages = virtual address space / page size.
Number of physical frames = physical memory / page size.
Process pages = process size / page size, rounded upward.
Offset bits = ceiling of log base two of page size.
Page number bits = ceiling of log base two of virtual pages.
Frame number bits = ceiling of log base two of physical frames.
Flat page table size = number of virtual pages × entry size.
Unused last page bytes = allocated process page bytes − process size.
Effective access time = hit ratio × hit time + miss ratio × miss time.
Sample physical address = frame number × page size + offset.
How to Use This Calculator
Enter the virtual memory size first. Then enter the physical memory size. Choose matching units for both values.
Add the page size and entry size. These two values control the number of entries and the table memory cost.
Enter the process size to estimate pages used by one process. Add the number of page table levels for a multi-level estimate.
Use the TLB fields to estimate average access time. Add a sample virtual address and mapped frame to test translation.
Press Calculate to view results below the header. Use the export buttons to save the same result as a CSV or PDF file.
Understanding Page Table Formula Calculations
What This Calculator Measures
Page table work starts with a simple idea. A program uses virtual addresses. Hardware maps them to physical frames. This calculator shows that mapping with clear numeric steps. It estimates pages, frames, offset bits, table entries, and memory overhead. It also checks a sample address translation. This helps students test operating system formulas without slow manual work.
Why Page Size Matters
Page size changes almost every result. A small page creates more pages. That can increase the page table size. A large page creates fewer pages. It can also increase internal fragmentation. The calculator reports the unused part of the final page. It also gives maximum and average waste. These values help compare different paging designs.
Address Bits and Table Entries
The offset bits identify a byte inside one page. Page number bits identify the virtual page. Frame bits identify the physical frame. Together, these values describe the address layout. When the page size is a power of two, the bit split is exact. When it is not, the calculator uses ceiling log base two. That keeps the result safe for planning.
Flat and Multi-Level Tables
A flat page table reserves entries for the full virtual address space. This can be simple but large. A multi-level page table can allocate table pages only where mappings exist. The calculator estimates this by using entries per table page and the selected number of levels. It is an estimate, because real layouts depend on address distribution.
Access Time Study
The TLB fields estimate effective access time. A TLB hit needs lookup time and one memory access. A miss needs lookup time, page table walks, and the final memory access. Higher hit ratios reduce average time. This makes the tool useful for quick performance comparison. It connects storage overhead with access speed in one practical result.
FAQs
What is a page table?
A page table stores mappings between virtual pages and physical frames. The processor uses it during address translation.
What is page size?
Page size is the fixed block size used to divide virtual memory and physical memory into manageable parts.
How are offset bits calculated?
Offset bits are calculated with log base two of page size. The calculator rounds upward when needed.
What is a page table entry?
A page table entry stores frame information and control bits. It may include valid, dirty, and permission flags.
Why does page table size grow?
It grows when virtual pages increase or entry size increases. Larger virtual spaces usually need more entries.
What is internal fragmentation?
Internal fragmentation is unused space inside an allocated page. It often appears in the final process page.
What does TLB hit ratio mean?
It means the percentage of address lookups found in the TLB. A higher ratio usually improves access time.
Is the multi-level result exact?
It is an estimate. Real multi-level table size depends on address layout, sparse mappings, and operating system design.