# Thread: Area: Square Meters vs. Meters Squared

1. ## Re: Perceived Brightness Index

[Extract of post copied from here]

If I have 1,000 lumens, and I shine them in a beam that makes a solid 1 m2 circle of light on my target, I will see 1,000 lux.

If that same emitter is projecting a floody 10 m2 circle of light, I will only see 100 Lux....and it will look dimmer.

2. ## Re: Perceived Brightness Index

Originally Posted by TEEJ
If I have 1,000 lumens, and I shine them in a beam that makes a solid 1 m2 circle of light on my target, I will see 1,000 lux.

If that same emitter is projecting a floody 10 m2 circle of light, I will only see 100 Lux....and it will look dimmer.
You are confusing 10 sq.m. and 10 m^2.

In your second example of the floody beam, 10 m^2 is an area 10m x 10m, which is 100 sq.m. Each 1 sq.m. area will therefore see 10 lux, not 100.

Can I now claim the prize for pedant of the day? LOL

3. ## Re: Perceived Brightness Index

Originally Posted by DM51
You are confusing 10 sq.m. and 10 m^2.

In your second example of the floody beam, 10 m^2 is an area 10m x 10m, which is 100 sq.m. Each 1 sq.m. area will therefore see 10 lux, not 100.

Can I now claim the prize for pedant of the day? LOL
WHAT?!? 1 sq.m. and 1 m^2 are the same. 10m * 10m = 100 m^2 = 100 sq.m.

sq.m. is merely a different way of writing m^2.

4. ## Re: Perceived Brightness Index

WHAT?!? 1 sq.m. and 1 m^2 are the same. 10m * 10m = 100 m^2 = 100 sq.m.

sq.m. is merely a different way of writing m^2.
I'm afraid you are wrong.

1 sq.m. and 1 m^2 are the same, but 10 sq.m. and 10 m^2 are not the same at all.

10 sq.m. is 10 x 1 m in area; 10 m^2 is 10 x 10 m in area.

5. ## Re: Perceived Brightness Index

Originally Posted by DM51
I'm afraid you are wrong.

1 sq.m. and 1 m^2 are the same, but 10 sq.m. and 10 m^2 are not the same at all.

10 sq.m. is 10 x 1 m in area; 10 m^2 is 10 x 10 m in area.
If 1 sq.m and 1 m^2 are the same, then 10 sq.m. and 10 m^2 are also the same. Let's do the math:

1 sq.m. = 1 m^2

(multiply by 10 on both sides)

10 * 1 sq.m. = 10 * 1 m^2 =>

10 sq.m. = 10 m^2

Or we could look on wikipedia: http://en.wikipedia.org/wiki/Square_metre
Have a look in the first line of the table:

Name: square meter, Symbol: m^2

Trust me on this. I teach college level math and physics

6. ## Re: Perceived Brightness Index

10m x 10m = 10 x 10 x m x m = 10^2 x m^2= 100 m^2

7. ## Re: Perceived Brightness Index

In English, there is a difference between ten square meters and ten meters squared.

The first is an area covered by ten squares each measuring one meter by one meter; and the second is an area of ten meters by ten meters.

8. ## Re: Perceived Brightness Index

I think I see the problem now. The original poster wrote 10 m^2. You read this as (10 m)^2 ("10 meters squared"). However, the correct way of reading it is 10 (m^2), because power operations should always be evaluated before multiplication operations. And 10 (m^2) = 10 sq.m.

9. ## Re: Perceived Brightness Index

The original poster wrote 10 m^2. You read this as (10 m)^2 ("10 meters squared").
Correct; that's how I read it. And I think if we ask him, we'll find it's what he meant - an area 10m x 10m. Otherwise, he would have meant an area 3.33m x 3.33m. I rather doubt that is what he meant.

I think most people would take 10 m^2 to mean an area 10m x 10m.

10. ## Re: Perceived Brightness Index

Originally Posted by DM51
Correct; that's how I read it. And I think if we ask him, we'll find it's what he meant - an area 10m x 10m. Otherwise, he would have meant an area 3.33m x 3.33m. I rather doubt that is what he meant.

I think most people would take 10 m^2 to mean an area 10m x 10m.
Except physicists and mathematicians. The order of operands has to be obeyed. Just like the law of gravity

I believe he meant 10 (m^2) since that would make his calculation a correct one and result in I = 100 lux.

Let's leave it at that.

11. ## Re: Perceived Brightness Index

You're correct in that you win the pedant of the day award.

And, of course the math is what dictates what was meant. If it needed clarification, by golly, I think its about as clarified as possible.

Of course, as an excerpt from a larger thread, there was some context that was now assumed rather than shown.

The order of operands does cover the issue.

The context was in relation to how we judge the "brightness" of a flashlight, which of course is unit-less. I was essentially trying to point out that we don't see lumens, we see the end result of lux on the target.

After that, the same lumens can appear brighter or dimmer, depending upon the surface area its distributed across. The way users view perceived brightness is also influenced by whether, as an individual, they are primarily influenced by the hot spot, or the hot spot and corona, or the hot spot, corona and spill. Different people interpret these values differently when asked how "bright" a light is....and weight them according to their own (Typically subconscious) value system.

An individual's eye chemistry is also responding to different frequencies differently. Some lights put out more of one wavelength than another...so the same lumen output can cause a perceived difference in brightness, someone's eyes respond more, or less, to that emitter's spectrum. IE: You might SEE less even though a light is putting out more lumens, and, it is why two people might perceive a light's brightness differently.

When all of this is considered together, you can consider that a light might be available with two emitter options, and one might have a higher lumen output than the other....and be trying to decide if the added lumen out put will be enough to be worth springing for that option.

The problem with looking at the lumens again comes down to the typically different lens for the different LED. We see fairly consistently that the smaller LED's will throw more (Put the same lumens over a smaller surface area). We see a deeper/wider reflector as also tending to put the same lumens into a smaller patch of light on a target. So, when the light has a different LED, it also tends to have a different reflector, beam shape, etc, as well.

I see over and over again references to a light having to produce twice the lumens to be noticeably brighter. I also see in practice, that there is no such relationship, except by coincidence. In practice, there are too many variables to make that kind of assertion.

For context, I have an ordinary three-way incan GE 50-100-150 watt light bulb for a desk lamp. On the bulb's box, it lists the lumen output at 450-1150-1600 lumens for the three wattages.

I can definetely tell if the light is at the highest or middle settings, and when clicking it to 1600 lumens, it looks brighter than it did at 1150 lumens. That's a ~ 40% increase in lumens being perceived as brighter...not double, a mere 40%. Obviously, that 40% is enough of a difference that its worth having that third/high option on the bulb. LESS than 40% is also observable.

In practice, my 1,600 lumen lights ARE brighter to me than my 1,200 lumen lights, and my 2,000 lumen lights ARE brighter than my 1,600 lumen lights...and so forth. I can SEE MORE with the added light.

Where it would get tricky, is being able to tell what setting that three-way bulb might be at, if I were to walk into the room a day later, not knowing if it were on medium or high...without a reference point/comparison, such as clicking the light to change the brightness. The eye is bad at that: Side by side comparisons are a lot easier. I tried, and found I could do it IF I used a reference point, specifically, something I could see/resolve with the light on high, but not at medium...say a stapler located at the periphery in a shadow, etc.

If I could also see the stapler, it was on high, and so forth. If I didn't find a see/not see test/reference point, it was a lot harder to tell if I was on high or medium.

The conclusion I came to is that you can potentially see more with more light, even if you're bad at judging HOW MUCH more or less light that is.

12. ## Re: Area: Square Meters vs. Meters Squared

1x1=1
1/1=1

therefore, 10x10 should equal 10/10...right?

I think one issue is the language... 10 meter square is different (to me) than 10 meter squared. First is a total area of one "unit" (10 square meter), the second is one unit by one unit, or 10x10=100.

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