Component Precision and Accuracy

The number of decimal places you use in component arrays directly impacts color fidelity, especially during color space conversions and round-trip transformations. This guide explains how to maintain accuracy while avoiding unnecessarily bloated files.

Why Precision Matters

Color space conversions involve complex mathematical transformations. Insufficient decimal precision causes:

• Drift: Colors shift after round-trip conversion (sRGB → Lab → sRGB)
• Banding: Visible steps in smooth gradients
• Accumulation: Errors compound across multiple transformations
• Perceptual shifts: Subtle hue or saturation changes that become visible

For design systems shared across tools, precision ensures your brand colors remain consistent.

Recommended Decimal Places by Color Space

sRGB and DisplayP3

Recommendation: 4 decimal places

Example:

{
  "components": [0.9608, 0.8784, 0.8627]
}

Rationale:

• Ensures sub-0.4% precision per component
• Sufficient for representing 8-bit source data (255 levels)
• 4 decimals ≈ 12-bit effective precision (4096 levels)
• Matches typical color picker precision in design tools

Impact of lower precision:

• 2 decimals: Only 100 distinct levels → visible banding in gradients
• 3 decimals: Acceptable for draft work, but may cause drift in conversions
• 6+ decimals: Excessive for 8-bit workflows, increases file size unnecessarily

Practical Test

Convert #F5E0DC to components:

• 2 decimals: [0.96, 0.88, 0.86] → back to hex: #F5E0DB (off by 1)
• 4 decimals: [0.9608, 0.8784, 0.8627] → back to hex: #F5E0DC (exact)

Lab

Recommendation: 4-5 decimal places for L, a, b

Example:

{
  "components": [51.2345, 80.1234, -70.5678]
}

Rationale:

• Required for accurate round-trip conversions
• Lab is often an intermediate space (sRGB → Lab → OKLCH → sRGB)
• a/b values are unbounded; precision prevents cumulative drift
• Critical for maintaining perceptual accuracy (ΔE < 1.0)

Impact of insufficient precision:

• 2 decimals: Significant color shifts (ΔE > 2.0 common)
• 3 decimals: Acceptable for some workflows, but may fail scientific use cases
• 4-5 decimals: Ensures ΔE < 1.0 (imperceptible difference) in round trips

Critical for:

• Design systems with strict color fidelity requirements
• Scientific/technical color work
• Cross-media color matching (print + digital)
• Color difference calculations (ΔE 2000, ΔE 94)

Round-Trip Accuracy

Lab is commonly used as an intermediate space for conversions. If you're converting sRGB → Lab → OKLCH, insufficient Lab precision will corrupt the final OKLCH values even if OKLCH itself uses high precision.

OKLCH

Recommendation: 4-5 decimal places for L and C, 1-2 for H

Example:

{
  "components": [0.72045, 0.14523, 210.5]
}

Rationale:

• Lightness (L) and Chroma (C) require high precision (similar to Lab)
• Hue (H) is coarse-grained (360° scale); 1-2 decimals usually sufficient
• Ensures perceptual uniformity is preserved across conversions
• Critical for perceptual color scales (e.g., design system color ramps)

Component-specific guidance:

• L (Lightness): 4-5 decimals (0 ≤ L ≤ 1)
• C (Chroma): 4-5 decimals (C ≥ 0)
• H (Hue): 1-2 decimals (0 ≤ H < 360) — more precision adds little value

HSL

Recommendation: 0-2 decimals for H, 2-4 for S/L

Example:

{
  "components": [10, 0.56, 0.91]
}

Rationale:

• Hue (H): Coarse-grained (360° scale); integers often sufficient
• Saturation/Lightness (S/L): 2-4 decimals needed for accurate round trips
• HSL is typically a presentation format, not a storage format

Precision by component:

• H (Hue): 0-2 decimals (integer degrees are usually fine)
• S (Saturation): 2-4 decimals (0 ≤ S ≤ 1)
• L (Lightness): 2-4 decimals (0 ≤ L ≤ 1)

HSL as Storage Format

HSL is popular for designer-facing tools, but it's not perceptually uniform. If storing authoritative color values, consider sRGB or OKLCH instead, and provide HSL in altRepresentations for convenience.

sRGB-linear-extended

Recommendation: 4-5 decimal places (may be unbounded)

Example:

{
  "components": [1.2345, -0.0678, 0.8901, 0.5]
}

Rationale:

• Linear light requires high precision for HDR workflows
• Values can exceed 1.0 (HDR) or be negative (wide-gamut)
• Used for physically accurate compositing
• Precision requirements similar to sRGB but with unbounded range

Alpha Channels

Recommendation: 2-4 decimal places (all color spaces)

Example:

{
  "components": [1.0, 0.5, 0.2, 0.85]
}

Rationale:

• Transparency typically doesn't require extreme precision
• 2 decimals = 100 levels (usually sufficient)
• 4 decimals matches other component precision (consistency)
• Perceptual difference in alpha is less critical than in color

Testing Round-Trip Accuracy

Here's how to verify your precision is sufficient using JavaScript and colorjs.io:

import Color from "colorjs.io";

// Original sRGB color
const original = new Color("srgb", [0.9608, 0.8784, 0.8627]);

// Convert to Lab and back
const lab = original.to("lab");
const roundTrip = lab.to("srgb");

// Calculate perceptual difference
const deltaE = original.deltaE(roundTrip, "2000");
console.log(`ΔE 2000: ${deltaE.toFixed(4)}`);

// ΔE < 1.0 = imperceptible difference (good!)
// ΔE 1.0-3.0 = noticeable under scrutiny
// ΔE > 3.0 = clearly visible difference (bad!)

Interpreting ΔE 2000 values:

• < 1.0: Imperceptible difference (excellent precision)
• 1.0-2.0: Perceptible only under close comparison (acceptable for most use cases)
• 2.0-3.0: Noticeable difference (marginally acceptable)
• > 3.0: Clearly visible difference (insufficient precision)

Rule of Thumb

If round-trip ΔE 2000 exceeds 1.0, increase decimal precision by one place and test again.

Common Pitfalls

Over-Precision

Problem: Using 8+ decimal places from floating-point calculations

Example:

{
  "components": [0.96078431372549, 0.87843137254902, 0.86274509803922]
}

Solution: Round to 4 decimals — additional precision adds no value for 8-bit workflows.

Under-Precision

Problem: Using 2 decimals for Lab values

Example:

{
  "components": [65.0, 30.5, -18.2] // Lab with insufficient a/b precision
}

Solution: Use 4-5 decimals for Lab/OKLCH to prevent drift.

Inconsistent Precision

Problem: Mixing high and low precision within a palette

Example:

{
  "colors": [
    { "components": [0.96, 0.88, 0.86] }, // 2 decimals
    { "components": [0.9608, 0.8784, 0.8627] } // 4 decimals
  ]
}

Solution: Standardise precision across your palette for consistency.

Precision vs File Size

File Size Impact

For a 100-color palette (sRGB, 3 components each):

Precision	Example Value	File Size Estimate
2 decimals	0.96	~1.2 KB (baseline)
4 decimals	0.9608	~1.6 KB (+33%)
6 decimals	0.960784	~2.0 KB (+67%)
8 decimals	0.96078431	~2.4 KB (+100%)

Recommendation: 4 decimals strikes the right balance between accuracy and file size for most use cases. Use gzip compression for distribution (typically 60-70% reduction).

Summary Table

Color Space	Component	Recommended Decimals	Rationale
sRGB	R, G, B	4	Matches 8-bit source precision
DisplayP3	R, G, B	4	Matches 8-bit source precision
Lab	L	4-5	Critical for perceptual accuracy
Lab	a, b	4-5	Unbounded, prevents drift
OKLCH	L, C	4-5	Perceptual uniformity
OKLCH	H	1-2	Coarse-grained hue scale
HSL	H	0-2	Integer degrees usually fine
HSL	S, L	2-4	Saturation/lightness precision
sRGB-linear-extended	R, G, B	4-5	HDR requires precision
Alpha (all)	A	2-4	Transparency less critical

Next Steps

• Gamut mapping: Learn about converting between color spaces in the Gamut Mapping guide
• Color space selection: Choose the right color space for your workflow in the Choosing Color Spaces guide
• Technical reference: See component validation rules in the Color Representations spec