The Page Replacement Algorithm Calculator is an advanced online tool designed for students, developers, system designers, and computer science professionals to simulate page replacement strategies used in operating systems. By entering the number of frames and a page reference string, this calculator quickly computes page faults, hits, hit rate, and provides a clear, step-by-step visual breakdown of each memory state.
This tool helps users understand how memory management works internally, making it ideal for learning, debugging, and academic use in OS (Operating System) subjects.
What Is Page Replacement in Operating Systems?
Page Replacement is a process used by operating systems when physical memory (RAM) is full. When a new page needs to be loaded into memory but no free frame is available, the OS must decide which page to remove to make space—this decision follows a specific algorithm.
This choice directly affects:
- Memory efficiency
- Page faults
- Process execution time
- Overall system performance
Your calculator simulates these algorithms in real-time.
Why Use a Page Replacement Algorithm Calculator?
Manual calculation of page faults and hits is complex and time-consuming. A single-page reference string may require dozens of steps.
With this tool, users can:
- Instantly simulate FIFO, LRU, and Optimal
- Visualise frame-by-frame memory changes
- Learn how different algorithms behave
- Compare performance (faults, hits, and hit rate)
- Get accurate calculations for assignments and exams
Built with educational accuracy and clear step-by-step representation, this calculator is ideal for OS students and professionals.
Available Page Replacement Algorithms
Your calculator supports the three most commonly used algorithms:
1. FIFO – First In First Out
FIFO replaces the oldest loaded page in memory.
How It Works:
- Frames work like a queue
- The oldest entry is removed first
- Simple but not always optimal
Pros:
- Easy to understand and implement
Cons:
- May suffer from Belady’s anomaly (more frames → more faults)
2. LRU – Least Recently Used
LRU replaces the page that has not been used for the longest time.
How It Works:
- Tracks the timestamp or the position of each page
- The page with the oldest usage is replaced
Pros:
- More accurate than FIFO
- Reduces unnecessary faults
Cons:
- Requires tracking history
- More complex than FIFO
3. Optimal (Belady’s Optimal Algorithm)
Optimal replaces the page that will not be used for the longest time in the future.
How It Works:
- Looks ahead at future page references
- Selects the page with the farthest next use
Pros:
- Produces the minimum possible page faults
- Best algorithm for comparison/benchmarking
Cons:
- Not implementable in real systems
- Used only for theory and simulation
Technical Formulas Used in Calculation
1. Page Fault Count
Page Faults=∑(Pages not found in frames)\text{Page Faults} = \sum (\text{Pages not found in frames})Page Faults=∑(Pages not found in frames)
2. Hit Count
Hits=∑(Pages already present in frames)\text{Hits} = \sum (\text{Pages already present in frames})Hits=∑(Pages already present in frames)
3. Hit Rate
Hit Rate=(HitsTotal Pages)×100\text{Hit Rate} = \left( \frac{\text{Hits}}{\text{Total Pages}} \right) \times 100Hit Rate=(Total PagesHits)×100
4. Fault Rate
Fault Rate=100−Hit Rate\text{Fault Rate} = 100 – \text{Hit Rate}Fault Rate=100−Hit Rate
Each algorithm computes frame placements differently, following its own rules (FIFO queue rotation, LRU usage tracking, Optimal future index scan).
How the Page Replacement Algorithm Calculator Works
The calculator uses:
- Dynamic memory array
- Step-by-step simulation
- Internal history tracking
- Hit & fault detection
- Frame table rendering
Each step shows:
- Current page
- Frame state
- Whether a page fault occurred
- Updated hit/fault count
This makes the tool both analytical and educational.
How to Use the Calculator
Step 1: Enter Number of Frames
Example: 3, 4, or 5 frames.
Step 2: Enter Page Reference String
Example:7, 0, 1, 2, 0, 3, 0, 4
Step 3: Choose Algorithm
- FIFO
- LRU
- Optimal
Step 4: Click “Calculate”
You will instantly see:
- Page faults
- Number of hits
- Hit rate
- Step-by-step memory table
- Page replacement breakdown
Example Calculation
Input
- Frames = 3
- Algorithm = FIFO
- Pages =
7, 0, 1, 2, 0, 3, 0, 4
Output
- Page Faults: 6
- Hits: 2
- Hit Rate: 25%
- Detailed memory table showing each step
This helps users understand algorithm behaviour visually.
Applications of This Tool
This tool is useful for:
Students
OS assignments, lab programs, and exams.
Teachers
Teaching memory management with visual examples.
Developers
Understanding caching and memory optimisation logic.
System Engineers
Simulating page handling behaviour in real-world scenarios.
Benefits of Using This Calculator
- Accurate simulation of OS algorithms
- Saves time for students and professionals
- Clean and clear visual table layout
- Helps compare algorithms
- Supports three major algorithms
- Beginner-friendly
- Works directly in the browser (no installation needed)
FAQ – Page Replacement Calculator
1. What is a page fault?
A page fault occurs when the required page is not found in memory frames.
2. Which algorithm gives the minimum page faults?
Optimal always gives the least possible page faults.
3. Can I use this tool for assignments?
Yes, it provides accurate, educational outputs.
4. Does the calculator support large page strings?
Yes, it can handle long sequences efficiently.
5. Does LRU always perform better than FIFO?
Usually yes, but it depends on the reference pattern.
6. Why use a simulator instead of manual calculations?
Manual calculations take time and are error-prone; a simulator is instant and accurate.