LED Brightness Cheat-Sheet (lm, lux, mcd) + Ring Notes

• mcd = directional intensity (good for indicators).
• lm = total light output (good for illumination).
• lux = light on a surface.
• At 1 m, on-axis: lux ~ cd.
• A 180 mcd LED is an indicator, not a light source.
• Ring of 54 white LEDs at ~8.5 lm each -> ~459 lm total -> ~146 lux at 1 m on-axis (assuming wide spread). Usually run well below max for comfort and thermals.

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1) Units

• Lumens (lm): total light output in all directions.
• Candela (cd) / millicandela (mcd): intensity in a specific direction.
• Lux (lx): illumination on a surface (how bright it looks on a target).

At distance r (meters), the basic relation is:

$$
E_{\mathrm{lux}} = \frac{I_{\mathrm{cd}}}{r^{2}}
$$

At r = 1 m:

$$
E_{\mathrm{lux}} \approx I_{\mathrm{cd}}
$$

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2) Conversions you will use

Given a full viewing angle theta (in degrees), approximate solid angle:

$$
\Omega ;\approx; 2\pi!\left(1 - \cos\frac{\theta}{2}\right) \quad \text{[steradians]}
$$

From lumens to candela:

$$
I_{\mathrm{cd}} ;\approx; \frac{\Phi_{\mathrm{lm}}}{\Omega}
$$

From candela to lumens:

$$
\Phi_{\mathrm{lm}} ;\approx; I_{\mathrm{cd}} \cdot \Omega
$$

Millicandela shortcut at 1 m:

$$
E_{\mathrm{lux}} ;\approx; \frac{\mathrm{mcd}}{1000}
$$

Notes:

• Narrower beam -> higher cd on-axis without increasing total lumens.
• Diffusers improve uniformity but reduce peak cd and peak lux.

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3) How bright at 1 m (on-axis examples)

Example	Spec	Angle (full)	cd (approx)	lux @ 1 m (approx)	lm (approx)	What it feels like
Indicator LED	180 mcd	20 deg	0.18	0.18	0.017	Tiny status dot; no area lighting
Indicator LED	180 mcd	60 deg	0.18	0.18	0.15	Small indicator; visible up close
Indicator LED	180 mcd	120 deg	0.18	0.18	0.56	Still only an indicator
White SMD LED	8.5 lm	120 deg	~2.7	~2.7	8.5	Modest accent at 1 m
LED Ring (54 x 8.5 lm)	459 lm	120 deg	~146	~146	459	Bright accent / light wash
Flashlight (spot)	300 lm	20 deg	~3140	~3140	300	Intense hotspot
Bare bulb (omni)	800 lm	~360 deg	~64	~64	800	Gentle room illumination

Lux context: hallway ~50 lx, living room ~100 to 300 lx, desk work ~300 to 500 lx, overcast daylight ~1000 to 10000 lx.

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4) Why colored LEDs use mcd and white LEDs use lm

• Colored LEDs are commonly used as directional indicators, so vendors quote mcd (directional punch depends on angle).
• White LEDs are used for area illumination, so lumens communicate total light output better.

Bottom line: a 180 mcd colored LED is not bright at 1 m (about 0.18 lux on-axis). For colored light that actually illuminates, use RGB or RGBW parts specified in lumens, or mix white for output with color as accent.

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5) Your LED ring (current working spec, preliminary)

• LEDs: up to 66 (~4000 K) total. Layout supports 54 on the ring plus up to 12 near the center for a cruising mode. Final count may shift slightly with layout and thermal constraints.
• Drivers: four TLC5947 constant-current drivers (30 mA max per channel). One is master, three are slaves.
• Estimated power: about 6 W at 5 V under representative patterns (depends on current, PWM, and LED binning).
• Thermal monitoring: TMP117 for board temperature (I2C).
• Control interfaces: SPI for TLC5947 and I2C for TMP117.
• Connectivity: JST-XH connector on the rear PCB.
• Status: preliminary layout. Minor placement, routing, clearance, and DFM changes expected before final release.

Brightness takeaway:

• 54 x 8.5 lm ~ 459 lm total. With a wide spread, on-axis illuminance ~146 lux at 1 m.
• In practice, operate below 30 mA (for example 10 to 20 mA, or PWM <= 50 percent) for comfort and thermal headroom.
• A diffuser improves uniformity but may reduce peak lux by about 20 to 40 percent.

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6) Design scenarios

• Status or indicator ring at 0.5 to 1 m: 54 whites at reduced current are sufficient; enable inner 12 for extra pop if needed.
• Colored accent visible at ~1 m: avoid low-mcd parts; select RGB or RGBW with lumen ratings, or blend white + color.
• Thermals and longevity: keep junction temperature down using copper pours, thermal vias, and moderate drive currents.

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