chmod Permission Converter (Octal ↔ rwx)
Convert between octal (e.g. 755, 4755) and symbolic (e.g. rwxr-xr-x, rwsr-xr-x) Unix file-mode notations, with the matching chmod command shown live. The three permission triplets correspond to user / group / other, each holding read / write / execute bits, plus three optional special bits: setuid, setgid and sticky.
Permission matrix
| Read (r) | Write (w) | Execute (x) | |
|---|---|---|---|
| Owner (user) | |||
| Group | |||
| Others |
Special bits
Enter a valid octal mode (0–7777) or a 9-character rwx string.
chmod command
chmod 755 file Common modes:
Calculates Unix / POSIX permission bits. Does not cover ACLs, SELinux labels or Windows ACLs. On a directory, x means "enter" rather than "execute".
Formula
mode = setuid·4000 + setgid·2000 + sticky·1000 + (u_r·400 + u_w·200 + u_x·100) + (g_r·40 + g_w·20 + g_x·10) + (o_r·4 + o_w·2 + o_x·1) [octal]
- · r = 4, w = 2, x = 1. Sum the three bits per class to get a single octal digit 0–7.
- · The four-digit octal order is: special (setuid + setgid + sticky), user, group, other. For example, 4755 = setuid + rwxr-xr-x.
- · Lowercase s / t in the symbolic form means "special bit set AND execute set"; uppercase S / T means "special bit set but execute not set" — matches ls -l and stat exactly.
- · On a directory, x means "may enter / traverse". Without x, even read permission only lets you list names — you cannot cd in or read file contents.
- · Common modes: 600 private files / 700 private directories, 644 regular files / 755 executables and directories, 777 world-writable (rarely advisable), 1777 sticky shared directory (e.g. /tmp).
- · References: POSIX.1-2017 chmod(1) and stat(2); GNU coreutils chmod manual. This tool covers permission bits only — ACLs, SELinux labels and Windows ACLs are out of scope.
Frequently asked
When should I use 755 vs 644 vs 700?
Rule of thumb: 755 for executables and directories that others need to enter (owner full, others read/execute); 644 for regular files (owner read/write, others read-only); 700 / 600 for strictly private directories / files (owner only). SSH private keys must be 600 — OpenSSH refuses to load keys with looser modes — and ~/.ssh must be 700. Web roots are usually 755 with 644 for PHP/HTML files. World-writable 777 should be temporary debugging only; in production prefer group ownership with setgid, or use ACLs.
What do setuid, setgid and sticky bits actually do?
setuid (4000): an executable runs with the owner’s privileges — used by tools like /usr/bin/passwd and sudo that need brief privilege escalation. Modern Linux/BSD ignore it on shell scripts. setgid (2000): an executable runs with the file’s group, and on a directory it makes new files inherit the directory’s group — useful for shared-team folders. sticky (1000): on a directory, only the owner of each file (or root) can delete it — classic on /tmp and /var/tmp, which run as 1777. setuid/setgid on regular files is a real security risk and should be audited carefully.
Why does the symbolic form sometimes show s/S or t/T instead of x?
When setuid, setgid or sticky is set, the special bit reuses the matching execute slot: setuid reuses user-x, setgid reuses group-x, sticky reuses other-x. Lowercase s / t means both the special bit AND execute are set; uppercase S / T means only the special bit is set (execute is not). This is the same convention that ls -l and stat have used for decades, and this tool follows it exactly.
Can I paste the full 10-character string from ls -l?
Yes. The first character in ls -l output is the file type (- regular, d directory, l symlink, c/b device, etc.). This tool strips that prefix automatically and parses the remaining nine permission characters, so pasting "-rwxr-xr-x", "drwxr-xr-x" or "lrwxrwxrwx" directly into the symbolic field works as expected.
Related tools
Percentage Calculator
Percent of, percent change, and percent add/subtract in one.
GCD & LCM Calculator
Enter 2–6 positive integers to get the greatest common divisor (HCF / GCD) and least common multiple (LCM), with the Euclidean step chain shown.
Average Calculator (Mean / Median / Mode)
Enter a list of numbers to get the mean, median, mode, range plus standard deviation, variance and total.
Quadratic Equation Solver
Enter the coefficients of ax² + bx + c = 0 to find the real or complex roots, discriminant and vertex.
Password Strength (Entropy) Calculator
Estimate a password's bit entropy, brute-force time and strength tier. All computation happens in your browser.
Scientific Notation Converter
Convert between standard decimal numbers and scientific notation, with significant figures and order of magnitude.
Permutations & Combinations (nPr / nCr) Calculator
Compute permutations P(n,r), combinations C(n,r) and factorial n! — useful for probability problems, lottery odds and combinatorics homework.
Standard Deviation Calculator
Paste a list of numbers to compute mean, median, sample and population variance and standard deviation — with the working shown.
Triangle Calculator (SSS / SAS / ASA)
Solve a triangle from 3 sides, 2 sides + 1 angle, or 2 angles + 1 side — area, perimeter and remaining parts via the law of sines / cosines.
Pythagorean Theorem Calculator
Given any two sides of a right triangle (two legs, or one leg plus the hypotenuse), instantly find the third side, area, perimeter and the two non-right angles.
Circle Calculator (radius / diameter / circumference / area)
Enter any one of radius, diameter, circumference or area to get the other three — useful for design, engineering and DIY.
Roman Numeral Converter
Two-way conversion between Arabic numbers (1–3999) and Roman numerals (I, V, X, L, C, D, M) — handy for typesetting, chapter titles and homework.
Slope & Line Equation Calculator (y = mx + b from Two Points)
Enter two points (x₁, y₁) and (x₂, y₂) to instantly get the slope, y-intercept, line equation y = mx + b, distance, and midpoint — a classroom staple for algebra and coordinate geometry.
Birthday Paradox Calculator
Enter group size n to see the probability that at least two people share a birthday — the classic birthday problem.
Logarithm Calculator (log / ln / log₂ / any base)
Compute logₐ(x) for any base — natural log (ln), common log (log₁₀), binary log (log₂) and a custom base, with the change-of-base steps shown.
Z-Score (Standard Score) Calculator
Enter a value, the mean and the standard deviation to compute the z-score and the corresponding normal-distribution percentile and probabilities.
Screen Pixel Density (PPI) Calculator
Enter the screen resolution and diagonal size to get pixel density (PPI), real width/height, dot pitch and total pixel count.
Hong Kong Mark Six Odds Calculator
Enter the number of tickets / selections and see the actual probability of hitting first, second … prizes in a Mark Six (6-of-49) draw.
Decimal to Fraction Converter
Convert any decimal (including repeating decimals) to a simplified fraction and a mixed number.
Sphere Volume & Surface Area Calculator
Give a sphere any one of radius, diameter, surface area or volume and instantly get the other three — plus the great-circle circumference and area.
Cylinder Volume & Surface Area Calculator
Enter the radius and height of a cylinder to get volume (π r²h), lateral surface, base area and total surface area.
Permutations (nPr) Calculator
Compute nPr — the number of ordered arrangements of r items chosen from n — alongside n!, r! and the related combination nCr.
Prime Factorization Calculator
Factor any integer from 2 up to 10¹² into primes, see the canonical exponent form, count and list all divisors.
Geometric Mean Calculator
Compute the n-th root of the product of n positive numbers — the right average for growth rates, returns and ratios — alongside the arithmetic mean for comparison.
Fibonacci Sequence Calculator
Enter any integer n from 0 to 1500 to instantly compute F(n) and F(n−1) with BigInt precision, the consecutive-term ratio (converging to the golden ratio φ) and the first 30 terms of the sequence.
Dice Roll Probability Calculator
Pick the number of dice, sides (d4 / d6 / d8 / d10 / d12 / d20) and a target sum to compute the probability of rolling exactly that total, at least, or at most.
Arithmetic Series Calculator
Enter first term a, common difference d and number of terms n to compute the nth term aₙ and the partial sum Sₙ = n/2·(2a + (n − 1)d).
Survey Sample Size Calculator
Enter confidence level, margin of error, expected proportion (and optional population size) to compute the survey sample size you need.
Geometric Series Sum Calculator
Enter the first term a, common ratio r and number of terms n to find the sum of the first n terms of a geometric series — plus the infinite-series sum when |r| < 1.
Cone Volume & Surface Area Calculator
Enter base radius and height to get the cone volume, slant height, lateral, base and total surface area.
Music Note Frequency Calculator
Pick a note (C, C♯, D, …), octave and tuning reference A4 (440 Hz by default) and the tool returns the frequency in Hz, the wavelength in air and the MIDI note number via f = A4 × 2^((n − 69)/12).
Linear Interpolation Calculator (Lerp)
Enter two known points (x₁, y₁) and (x₂, y₂) and a target x to instantly read off y via y = y₁ + (x − x₁)(y₂ − y₁)/(x₂ − x₁) — the tool flags whether your x sits inside the two points (interpolation) or outside (extrapolation).
Trapezoid Area Calculator
Enter the two parallel sides and height of a trapezoid to get its area, midsegment length and perimeter when the legs are known.
Binomial Probability Calculator
Enter the number of trials n, the per-trial success probability p and a target number of successes k to get P(X = k), P(X ≤ k), P(X ≥ k) along with the distribution mean and standard deviation.
Pearson Correlation Coefficient Calculator
Paste two parallel data series (X and Y) and get the Pearson correlation coefficient r, r², the best-fit line slope and intercept, and the sample means and standard deviations.
Confidence Interval for the Mean Calculator
Enter the sample mean, sample standard deviation, sample size and confidence level to compute a confidence interval for the population mean using the t (or z) distribution, with margin of error and standard error.
Cohen's d Effect Size Calculator
Enter the means, standard deviations and sample sizes of two groups to compute Cohen's d and Hedges' g effect sizes, classified per Cohen 1988 as trivial / small / medium / large.
Modulo (Remainder) Calculator
Enter dividend a and divisor n to compute the quotient and remainder a mod n. The truncated (C / JavaScript %), floored (Python / mathematical) and Euclidean conventions are shown side by side so the negative-input differences are obvious.
Vector Magnitude & Direction Calculator (2D / 3D)
Enter 2D or 3D vector components (x, y, z) to compute the magnitude, unit vector and direction angles.