A blockchain fork occurs when a blockchain diverges into two separate paths. This can happen for various reasons, leading to different versions of the transaction history.
Forks are an inherent part of decentralized systems like blockchains, as different participants (miners or validators) may not always agree on the exact order of transactions or the next valid block.

There are primarily two types of blockchain forks:

Soft Forks: These are backward-compatible changes to the blockchain protocol. Nodes that don't upgrade to the new rules will still see the new blocks as valid, though they might not be able to fully validate them. Soft forks typically require a majority of the network to adopt the new rules to be successful.

Hard Forks: These are backward-incompatible changes, meaning that nodes running the old software will not recognize blocks created by nodes running the new software. This results in two distinct blockchains operating simultaneously. Hard forks often lead to the creation of a new cryptocurrency if a significant portion of the community continues to support the old chain.

Natural forks, also known as unintentional or temporary forks, primarily occur due to network latency and the decentralized nature of blockchain mining. When two miners discover a valid block at roughly the same time, these blocks might propagate to different parts of the network simultaneously.
This leads to a temporary split where some nodes see one block as the latest, while others see the other. Eventually, as more blocks are mined, one chain becomes longer, and the network converges on that chain, abandoning the shorter one. The orphaned blocks and transactions are then typically re-added to the mempool for inclusion in the winning chain.

A malicious fork is an intentional attempt to manipulate the blockchain's history, often for nefarious purposes like double-spending.
This typically involves an attacker gaining control of a significant portion of the network's mining power (hash rate). A 51% attack is a scenario where a single entity or group controls more than 50% of the network's total hash rate. With this majority, the attacker can:

- Prevent new transactions from gaining confirmations.
- Stop other miners from mining valid blocks.
- Reverse their own transactions, enabling double-spending.

By secretly mining a longer chain and then releasing it, the attacker can effectively rewrite recent transaction history, making previously confirmed transactions invalid on the main chain.
The probability of a successful malicious fork increases significantly with the attacker's hash rate and decreases with the number of confirmations a transaction has received.

Network propagation delay refers to the time it takes for a newly mined block to be transmitted and received across the entire blockchain network. A higher propagation delay increases the likelihood of natural forks.
If blocks take longer to reach all nodes, there's a greater chance that different miners will find and build upon different valid blocks simultaneously, leading to temporary chain splits. Efficient network infrastructure and low latency are crucial for minimizing natural fork occurrences and maintaining a consistent view of the blockchain.

Confirmation blocks are crucial for ensuring the finality and security of transactions on a blockchain.
When a transaction is included in a block, and subsequent blocks are mined on top of it, each new block adds a
layer of security. The more confirmations a transaction has, the more difficult and costly it becomes for an attacker to reverse it.
For instance, in Bitcoin, six confirmations are generally considered sufficient for high-value transactions, as the probability of a successful double-spend attack after six confirmations becomes astronomically low.

The number of active miners can influence the probability of natural forks. In a network with many miners, there's a higher chance that two or more miners will find a valid block at nearly the same time, leading to temporary forks.
However, a larger, more decentralized mining pool also contributes to overall network security and resilience against malicious attacks, as it makes it harder for any single entity to gain a majority hash rate.

The analysis time window defines the period over which the fork probability is calculated. It helps to understand the likelihood of forks occurring within a specific timeframe.
For natural forks, a longer time window might show a higher cumulative probability of temporary forks, as these events are expected to happen periodically due to network latency. For malicious forks, the time window can represent the duration an attacker attempts to maintain a secret chain or the period during which a double-spend attack is attempted.

The Blockchain Fork Probability Calculator provides a quantitative assessment of various factors influencing network security. By inputting parameters such as network hash rate, block time, propagation delay, and potential attacker hash rate, users can:
- Assess Natural Fork Risk: Understand the likelihood of temporary chain splits due to network conditions.
- Evaluate Malicious Attack Vulnerability: Determine the probability of a successful 51% attack or double-spend given an attacker's hash rate.
- Optimize Confirmation Times: Identify the optimal number of confirmations needed for transactions based on the network's security posture.
- Gain Insights into Network Health: Monitor key metrics that indicate the overall decentralization and resilience of the blockchain.
This tool empowers users, developers, and researchers to make informed decisions regarding blockchain security, transaction finality, and network design.

While the calculator provides probabilities based on current and hypothetical network parameters, it cannot predict specific future forks with certainty. Blockchain networks are dynamic, and factors like hash rate distribution, network topology, and miner behavior can change rapidly.
The calculator is a valuable tool for understanding the likelihood and risk associated with forks under given conditions, helping to assess potential vulnerabilities and inform strategic decisions rather than forecasting exact events.