Saddle-stitch booklet: Sheets are nested and stapled through the centre fold. Like a magazine -- the first and last pages are printed on the same outer sheet, back-to-back.

Signature: A nested group of sheets. "4 sheets per signature" means 4 physical sheets folded together, giving 16 page positions (4 sheets × 2 sides × 2 pages per side).

Spine Gap: Blank space at the centre fold reserved for the staple. Increase for thicker paper.

Registration Marks: Dashed fold guide line + "Sig. N · Sheet N of N" label (so you know assembly order) + 4 alignment dots along the spine.

Three Steps:
① Resize -- Pages stretched to fill exactly half the canvas width.
② Impose -- Pages reordered onto A4-landscape sheets in correct saddle-stitch sequence.
③ Marks -- Fold guides, labels, and binding dots drawn on every sheet.

What it does: Joins multiple PDF files into one output document, appending pages in the queue order shown below. Use Up/Down to reorder before running. You can add the same file twice to duplicate its contents.

Custom Ranges -- e.g. 1-5, 8, 10-12 -- each token = one output file.
Uniform Interval -- chop into equal N-page batches.
Granular Extraction -- e.g. 3, 7, 12 -- each page becomes its own file. Use "Preview Splits" to verify before running.

Lossless only: Re-serialises the PDF with DEFLATE compression and packs objects into clustered streams. Removes structural bloat and orphaned objects. Does not downsample images -- for large image-heavy PDFs, reductions are typically 5–20%. Best results on PDFs with lots of uncompressed text or metadata.

N-up printing places N source pages onto one output sheet in a grid. "2-up" = 2 pages side by side; "4-up" = 2×2 grid. Useful for printing lecture slides compactly, creating study note booklets, or proof-printing a large document cheaply.

Cell size: (sheet width − 2×margin − (cols−1)×spacing) ÷ cols, and similarly for height.

Click a row to select it (highlighted gold), then use the action buttons. Clone duplicates a page so it appears multiple times. Reset restores the original order. The original file is never modified.

DPI (Dots Per Inch) controls sharpness:

• 72–96 DPI -- screen/web only, small file
• 150 DPI -- presentation quality
• 200–300 DPI -- suitable for print

PNG = lossless, larger, ideal for text-heavy pages. JPEG = lossy, smaller, better for photo-heavy pages.

Note: This tool requires pdf.js which loads from CDN on first use (or from ./js/pdf.min.js if you have it locally).

Opacity: 100% = fully visible. 15–30% = typical transparent stamp that doesn't obscure the content behind it.

Rotation: −45° gives the classic diagonal watermark look across the page. 0° = horizontal.

Position -- Diagonal Centre: The watermark text is trig-corrected so its visual midpoint lands exactly at the centre of the page regardless of rotation angle.

Image Watermark: Upload a PNG (with transparent background works best) or JPEG logo. Use the Scale slider to control its size on the page. The image is placed at the same position as the text watermark.

Where watermarks live in a PDF -- and which strategy removes each:

Strategy 1 -- Strip Annotations: Removes the Annots array from each page. Handles watermarks added as stamps by Acrobat, foxit, or similar tools. Very effective, non-destructive.

Strategy 2 -- Text Redaction: Searches each page for your keyword text and covers it with a white rectangle. Requires pdf.js for accurate text positioning. Falls back to a centre-stripe cover if pdf.js is unavailable.

Strategy 3 -- Image Overdraw: Covers large background images (above a pixel threshold) with a white rectangle. Targets watermarks that are full-page JPEG/PNG backgrounds. Does not delete the image data, just hides it.

Strategy 4 -- Vector Neutralize: Decompresses PDF content streams using pako (loaded from CDN), finds grey color operators (fill/stroke commands like 0.85 0.85 0.85 rg) and replaces them with white. Targets watermarks drawn as grey vector shapes. Ported from the Python notebook's obliterate_remaining_watermark() function.

Honest limit: Watermarks baked directly into the original page creation cannot be removed without re-rasterizing the page (needs Ghostscript/server). Always run the Scan first.

Strips RC4/AES encryption from a password-protected PDF. You must supply the correct password -- this tool does not crack or guess passwords.

Common passwords in India:

• Aadhaar PDF → your date of birth in DDMMYYYY format (e.g. 15081998)
• Bank statements → your account number or date of birth
• ITR/TDS → PAN number in uppercase

Owner-password-only files (restrict printing but not opening) are handled automatically -- leave the password blank.

Adds a visual rubber-stamp graphic -- a double-bordered rectangle containing a ✓ checkmark, the selected text, and optionally the current date. Commonly used for self-attesting Aadhaar cards, mark sheets, or government documents before submission.

This is a visual mark only -- not a cryptographic digital signature. For legally valid digital signatures, use Aadhaar eSign or a licensed Digital Signature Certificate (DSC) tool.

Quality %: Controls how much image data is discarded during JPEG/WebP encoding. 100% = no compression. 60–80% is the typical sweet spot -- visually near-identical but 50–70% smaller.
PNG: Lossless -- quality % has no effect. Reduce dimensions for PNG size reduction.
WebP: Google's modern format. Better quality-to-size ratio than JPEG. Widely supported in browsers.
Squoosh (link in nav bar) = Google's tool with additional codecs like AVIF and oxipng.

Pixels vs Physical Size: Physical size only has meaning when combined with DPI. Formula: pixels = size × DPI. Example: 3.5 cm at 200 DPI = 3.5 ÷ 2.54 × 200 ≈ 276 px.

Common exam/govt requirements:

• Photograph: 3.5 × 4.5 cm, 200 DPI, max 50 KB, JPEG
• Signature: 3.5 × 1.5 cm, 200 DPI, max 20 KB, JPEG

Target KB: The tool uses binary search on JPEG quality to achieve your target file size within ±5%.
Keep Aspect Ratio: Changing one dimension auto-scales the other proportionally.

Common Indian document photo sizes:

• Indian Passport: 51×51 mm, white or light-blue background
• Aadhaar/PAN: 35×45 mm, white background
• UPSC/SSC: 3.5×4.5 cm at 200 DPI (≈276×354 px)
• US Visa: 51×51 mm at 300 DPI (600×600 px)

Crop tips: Use the crop sliders to frame your face. Brightness helps if the background appears grey instead of white.

Threshold (50–254): Each pixel's luminance (brightness) is measured. Pixels brighter than the threshold become fully transparent. For dark ink on white paper, set to 200–230.

• If the signature looks too thin → reduce the threshold
• If white patches remain → increase the threshold

Output: A PNG with a transparent background (shown as a checkerboard in the preview). Place this PNG over any background colour in Word, PowerPoint, or PDF tools.

Images (JPEG, PNG, WebP): The canvas redraw method is the most thorough browser-available technique. It removes:

• EXIF -- camera model, lens, exposure, ISO, flash
• GPS -- latitude, longitude, altitude, timestamp
• Thumbnail -- the embedded preview image in EXIF
• XMP -- Adobe metadata block
• ICC colour profile reference (replaced with browser default)

PDF: Clears all standard document information fields: Title, Author, Subject, Keywords, Creator, Producer, Creation Date, Modification Date. Also removes the XMP metadata stream if one is present.

Note: The canvas redraw changes the colour profile to sRGB. For professional print work, this may affect colour accuracy. For everyday use (web, forms, WhatsApp) it makes no visible difference.

Variable: Use x in graph mode.
Functions: sin(x) cos(x) tan(x) log(x) log10(x) sqrt(x) abs(x) factorial(n)
Constants: pi e tau
Powers: x^2 or x**2
Important: Write 2*x not 2x. Implicit multiplication is not supported.

Matrix: A rectangular grid of numbers. Written as m×n (m rows, n columns).
Square matrix: Same rows and columns (2×2, 3×3). Required for det, inverse, trace, eigenvalues, LU.
Determinant (det A): A single number summarising a square matrix. If det=0, the matrix is "singular" -- no inverse exists.
Inverse (A⁻¹): A×A⁻¹ = Identity. Only exists when det≠0.
RREF: Reduced Row Echelon Form. Used to solve systems of equations. Each row's leading entry is 1, and all other entries in that column are 0.
Eigenvalues (2×2 only): Values λ where A×v = λ×v. Found by solving the characteristic equation λ² − tr(A)λ + det(A) = 0.

Demo -- Solve 2x + y = 8 and x − y = 1:
Set Matrix A to 2 rows × 3 columns. Enter top row: 2, 1, 8. Bottom row: 1, -1, 1. Click RREF(A). The result gives x=3 (row 1: 1, 0, 3) and y=2 (row 2: 0, 1, 2).