About

Rendering an analog clock at arbitrary scales introduces non-trivial challenges in stroke-weight proportionality, numeral legibility, and tick-mark density. A naive CSS transform: scale(s) on a raster element produces blurred artifacts. This tool redraws the entire clock on a Canvas element at the target resolution, recalculating every dimension - hand length, stroke width, font size - as a function of the scale factor s. The base clock radius r = 120 px is multiplied by s ∈ [0.25, 4.0], yielding effective diameters from 60 to 960 px. Device pixel ratio compensation ensures crisp edges on HiDPI screens at every scale.

Practical applications include dashboard embedding at constrained sizes, kiosk displays requiring large faces, and accessibility scenarios where users need enlarged time readouts. The tool accounts for sub-pixel rendering, proportional hand tapering, and graduated tick marks. Note: browser canvas performance degrades above approximately 4000 px canvas width on low-end hardware, hence the 4.0× upper bound.

Formulas

Each clock hand angle is computed from the current time components. The hour hand incorporates both hours and minutes for smooth sweep.

θ_sec = s60 × 2π − π2

θ_min = m + s6060 × 2π − π2

θ_hr = (h mod 12) + m6012 × 2π − π2

All rendered dimensions are proportional to effective radius R = r_base × s, where r_base = 120 px and s is the scale factor.

Where: s = seconds (0 - 59), m = minutes (0 - 59), h = hours (0 - 23), θ = angle in radians measured clockwise from 12 o’clock position, R = effective drawing radius.

Reference Data

Scale Factor	Effective Diameter	Minute Hand Length	Hour Hand Length	Stroke Width	Font Size	Use Case
0.25×	60 px	22 px	16 px	0.5 px	4 px	Thumbnail / Widget
0.5×	120 px	44 px	32 px	1.0 px	7 px	Sidebar embed
0.75×	180 px	66 px	48 px	1.5 px	10 px	Compact dashboard
1.0×	240 px	88 px	64 px	2.0 px	14 px	Default desktop
1.25×	300 px	110 px	80 px	2.5 px	17 px	Presentation
1.5×	360 px	132 px	96 px	3.0 px	21 px	Meeting room display
2.0×	480 px	176 px	128 px	4.0 px	28 px	Wall clock / Kiosk
2.5×	600 px	220 px	160 px	5.0 px	35 px	Large signage
3.0×	720 px	264 px	192 px	6.0 px	42 px	Accessibility / Low vision
3.5×	840 px	308 px	224 px	7.0 px	49 px	TV / Monitor display
4.0×	960 px	352 px	256 px	8.0 px	56 px	Full-screen kiosk

Frequently Asked Questions

The canvas is rendered at the device's native pixel ratio (window.devicePixelRatio). On displays with a DPR of 1, scaling above 2.0× may reveal anti-aliasing artifacts. The tool compensates by multiplying the internal canvas resolution by the DPR, but extremely high scales on low-DPR monitors will approach the limits of the GPU rasterizer.

All stroke widths, hand lengths, and font sizes are computed as linear functions of the effective radius R = 120 × s. This maintains visual proportionality. The hour hand width, for example, is always R × 0.035, ensuring it never becomes illegibly thin at small scales or disproportionately thick at large ones.

At 4× scale with a DPR of 2, the canvas pixel buffer reaches approximately 1920 × 1920 pixels. Each frame clears and redraws roughly 80 path operations. On modern hardware this consumes under 2 ms per frame - well within the 16.67 ms budget for 60 fps. Older mobile GPUs may drop to 30 fps above 3× scale.

The analog face always displays 12-hour positions (1-12) since a 24-hour analog face would halve the angular separation between hours from 30° to 15°, making the dial harder to read. The digital readout below the clock can be toggled between 12-hour and 24-hour format independently.

Canvas implementations across browsers have a maximum buffer size (commonly 4096 × 4096 or 16384 × 16384 pixels depending on GPU). At 4.0× with a base of 120 px radius and DPR of 2, the buffer is 1920 × 1920 - safely within limits. Allowing arbitrary scales risks a silent canvas failure where nothing renders.

By default the second hand uses continuous sweep, recalculating its angle every animation frame using Date.getSeconds() + Date.getMilliseconds() / 1000. You can toggle to discrete tick mode, where the hand snaps to integer second positions - matching traditional quartz clock behavior.