What each of the three measures
The lumen measures all the light leaving a source, added up across every direction it reaches. It is the figure on the bulb's box, which is why it is what compares one bulb with another.
The candela measures the light going in one particular direction. A bulb and a spotlight can put out the same lumens with the spotlight showing far more candela, because it concentrates that flux into a narrow cone instead of spreading it round the room. It is the unit of torches, where what gets advertised is reach.
The lux measures the light landing on a surface: one lumen spread over one square metre is one lux. It is the only one that matters where you actually need to see, and it is what light meters and phone apps read.
Why there is no conversion factor
Ω = 2π × (1 − cos(θ/2)) · lm = cd × Ω · lx = cd ÷ d²
Metres and feet have a factor because they measure the same thing. These three do not, because they measure different things, and moving between them needs geometry: the beam angle to turn candela into lumens, and the distance to turn candela into lux. A page that hands you a fixed lumen-to-lux equivalence is assuming a surface without saying so.
The solid angle is what bridges them. It is measured in steradians and is the share of a sphere the beam covers: a whole sphere is 4π ≈ 12.57 sr, and a 60° spot barely 0.84. Watch the formula, because the classic mistake is putting the whole angle inside the cosine instead of half of it: the cone opens that much on each side of the axis, and mixing it up multiplies the answer by four.
The formulas, to do it by hand
- Solid angle. For a 60° beam: cos(30°) = 0.866, so Ω = 2π × (1 − 0.866) = 0.84 sr.
- Candela to lumens. 1,000 cd × 0.84 sr = 842 lm.
- Candela to lux. 1,000 cd ÷ 2² = 250 lx at two metres.
- The check. Those 842 lm spread over the 3.37 m² the cone covers at two metres come back to the same 250 lx. If the two routes disagreed, one of them would be wrong.
What is worth knowing
Comparing bulbs by watts stopped making sense when LEDs arrived. The watt measures what it draws, not what it gives, and what links the two is luminous efficacy: an incandescent runs about 13 lm/W and an ordinary LED 90 or 100, so the same wattage gives seven times the light. That is why boxes print the lumens large: 800 lm is what the old 60 W bulb used to give.
And a warning about torches: when a maker quotes candela or a range in metres, they are measuring the brightest point at the centre of the beam, not the useful light. Two torches with the same lumens can advertise wildly different reach purely because one beam is tighter. If what you want is how much light a room needs, that is a different sum and the lighting calculator does it, starting from the square metres and what the room is for.