Bayes' theorem is a fundamental principle in probability theory that describes how to update the probability of a hypothesis based on new evidence. The theorem is expressed as: P(A|B) = P(B|A) · P(A) / P(B), where P(A) is the prior probability (initial belief before evidence), P(B|A) is the likelihood (probability of evidence given the hypothesis), P(B) is the marginal probability of evidence (total probability), and P(A|B) is the posterior probability (updated belief after evidence). This theorem is widely used in statistics, machine learning, medical diagnostics, spam filtering, and decision-making. It provides a mathematical framework for reasoning under uncertainty. The calculator also computes Bayes Factor (likelihood ratio), which quantifies the strength of evidence, and prior/posterior odds, which help interpret the results in terms of betting odds or risk assessment.
Numbers & Codes Calculators
Vigenère Cipher Calculator – Encryption & Decryption Tool
What is the Vigenère Cipher?
The Vigenère cipher is a method of encrypting alphabetic text by using a simple form of polyalphabetic substitution. It was invented by the French diplomat Blaise de Vigenère in the 16th century, though it was incorrectly attributed to him — the cipher was actually first described by Giovan Battista Bellaso in 1553.
The cipher uses a keyword to shift letters of the plaintext. Each letter of the keyword determines the shift for the corresponding letter of the plaintext:
Ci = (Pi + Ki) mod 26
Where Ci is the ciphertext letter, Pi is the plaintext letter, and Ki is the keyword letter (A=0, B=1, ..., Z=25). The keyword is repeated to match the length of the plaintext.
The Vigenère cipher was considered "le chiffre indéchiffrable" (the unbreakable cipher) for centuries because it resists simple frequency analysis attacks. However, it was eventually broken in the 19th century by Charles Babbage and Friedrich Kasiski using the Kasiski examination and frequency analysis of repeated key patterns.
Key features of this calculator:
- Encryption — converts plaintext to ciphertext using the keyword
- Decryption — converts ciphertext back to plaintext using the same keyword
- Preserves case — uppercase stays uppercase, lowercase stays lowercase
- Non-alphabetic characters — spaces, numbers, and punctuation remain unchanged
The Vigenère cipher is still used today in recreational cryptography and as an educational example of polyalphabetic substitution ciphers.
Number to Words Converter – Spell Out Numbers & Amounts
A number-to-words converter transforms numerical digits into their written word form. This is essential for legal documents, contracts, invoices, checks, and financial reports where numbers must be expressed in words to prevent fraud and ambiguity. The theoretical conversion follows a place-value system: each digit group (units, thousands, millions, etc.) is converted separately using language-specific naming conventions. For monetary amounts, the integer part is spelled out followed by the currency, and the decimal part (cents) is expressed as a fraction over 100. The converter handles numbers up to trillions and supports decimal values. This tool follows English grammar rules, including proper hyphenation for compound numbers (e.g., twenty-one) and correct pluralization of hundred, thousand, etc. All conversions are performed instantly with precise accuracy.
Percentage Calculator – Find Percentage of Any Number
A percentage represents a fraction of 100. It is a way to express a number as a part of a whole. The basic formula for calculating what percentage one number (A) is of another (B) is: (A / B) × 100 = percentage. For example, if you have 50 apples out of 200, the percentage is (50/200) × 100 = 25%. Conversely, to find a percentage of a number, multiply the number by the percentage and divide by 100: (percentage × number) / 100 = result. This tool performs both operations quickly and accurately. Percentages are used everywhere: in finance for interest rates and discounts, in statistics for data analysis, in education for grades, and in everyday life for tips and taxes. Understanding percentages is essential for making informed decisions in many areas of life.