Calculators:

[leonski]

hifi is largely a numbers game.    And numbers ARE confusing.    What do they all mean?    How are they arrived at?    Will a 100 watt amp really play louder than a 80 watt amp?
(not necessarily)

So, to get things rolling, here is a simple to use ONLINE calculator to help straighten out the most mis-used terms in speaker technology.    'Efficiency' and  'Sensitivity'.      Most persons incorrectly use these 2 terms
interchangeably.     Here is a calculator so you can really get a grip on the difference and why sensitvity may be the better 'measure' of how well a speaker turns electricity into sound.   And it ain't pretty.

www.sengpielaudio.com/calculator-efficiency.htm

I will periodically add either calculators or a simple way to DO a calculation (Put that scientific calculator on your iPhone to good use!) or even link an article with a scientific basis.

As usual, good numbers, (whatever THAT means) is no guarantee of good sound and the opposite is also true.

[leonski]

another number which gets people all excited is power. A frequent question would be something like: 'I have an amp of 200 watts but think I need more power. Would 300 watts be any better?'

Here's the math part, without getting into headroom and 'quality' in which either amp may simply sound better or drive the speakers in question better. I'll just deal with power, as if the amps were equal EXCEPT for that.

Here's the Math part:

To compute DB difference in the amps? Start by dividing 300/200 (Pamp1 / Pamp2) In this case, the number is 1.5
Now? On your SCIENTIFIC calculator, press 'log' and you'll get 0.176 THAN? Simply multiply by 10 (ten) and get 1.76db difference. 1.7 is close enough for government work. After all? The ear is supposed to be good to 1db, so you CAN hear the difference between amps.
But not likely in normal use.
To get 2x volume level? DOUBLE the power or 3db.
The math: 400watts new amp. 200 for your current amp. 400/200=2 10log (2) is 3.01 or 3db.
For 10x the level or +10db? You need 10x the power, too.
The math: 200 watts, original amp 2000 watts for 10db 'louder'. 2000/200 = 10 10log (10) = 10db increase.

As can be seen, getting loud requires a LOT of power. Clean Power. Of course, 200 watts continuous with 2000 watt peaks is nutty, but still, for reasonably sensitive HT speakers? 10 watts continuous and 100 watt peaks? OUCH!
And for 20db peaks which ARE out there, on some effects laden movies and some music? Power of 100x gives 20 db. I'll leave the math up to YOU.

[pknaz]

This is why most people only need a few watts. Most reasonable, or maybe I should say "main stream", speakers are in the 89-93db sensitivity range. You don't need much power to get you to permanent ear damage range, less than 1 watt, actually, depending on exposure length

[leonski]

Movie theaters are apparently set up for 85db with 20db peaks. For a 90" to 120" movie? You should be OK, right?

and yes, exposure LENGTH is key.

I was speaking with an audiologist at a recent airshow. MANY people and their KIDS were walking around with NO ear protection. I wore my fitted ($$$) plugs. Wife wore some 'cans' which I normally use when mowing the lawn.

Anyway? The guy said that African Tribesman of 50 to 60 years old have Better hearing than an American 1/2 his age.

[leonski]

www.mcsquared.com/wavelength.htm

Another potentially useful calculator. This one allows a frequency to wavelength conversion.

This kind of information is useful in designing listening areas. Speaker designers use it in baffle design and enclosure proportioning.

www.mcsquared.com/modecalc.htm

The ROOM MODE CALCULATOR is useful for deign and execution of listening rooms. Checking in advance for Standing Waves allows for the construction of rooms with fewer problems and less need of Room Treatments (not to the exclusion of such treatments, however)
Entering square floor plans shows why square rooms and rooms with dimensions that are multiples of one another should be avoided. Even a room with an 8 foot ceiling which is 16x24 will probably give problems.

[bitsandbytes]

Another good formula is for the apparent or perceived listening volume. A 10 decibel increase is required to get twice the perceived volume. That formula would be:

2^{(decibel change/10)}

An example is if trying to decide between a 110 wpc - or the same brand of amp with 170 wpc. Using the previously mentioned formula, need to calculate decibels first:

10 x log (watts/base reference in watts) = 10 x log (170/110) = 1.89 decibels increase

2^(1.89/10) = 2^.189 = 1.3997 = perceived listening volume increase of 14%. Meaning the 170 wpc amp will sound 14% louder before going into distortion than the 110 wpc amp.

The inverse square formula is used for calculating decibels lost with speaker distance. The sensitivity rating of speakers is taken with one speaker in an anechoic (non-reflective) chamber either 1 meter or 3 feet from the speaker. This formula:

10 x log [(3.28/measured distance in feet)²] Note: This 3.28 is with the sensitivity given at one meter with a one watt output. If taken at 3 feet, then the 3 is used instead of 3.28. Example, if sitting 8'8" from each speaker with the speaker sensitivity given at one meter, then:

10 x log (3.28/8.67)² = 10 x log .378² = 10 x log .143 = -8.45 db. The actual calculation without rounding off each step would be -8.4429 decibels.

Calculating the change in watts based on the change in decibels yields:

10(^{decibel change/10)}

This is useful when trying to figure out the watts required to achieve a certain level in decibels.

As only one speaker is used in sensitivity ratings, the second speaker has to be added. 10 x log (2/1) = 3.01 decibels increase. The room itself adds to the sound level. Paradigm uses a 3 db addition to differentiate between a live room and their anechoic chamber. This decibel increase will be different dependent upon room size, the hard and soft surfaces, windows, hollow doorways, openings to other rooms, and the broadband absorption and diffusion used. These will widely vary at each frequency too. For simplicity, will add +6 db for stereo and room adjustment.

An example putting this all together. If sitting 8 feet from the speakers with a speaker sensitivity of 90 decibels measured from 3 feet away, just how much power would be required to measure peaks on a SPL meter of 75 decibels?

10 x log (3/8)² = -8.52 db for distance. 89 - 8.52 (distance) + 6 db (room + stereo) = 86.48 decibels at one watt at the listening position. With 75 db required, this is a change of -11.48 decibels required. Using the formula to calculate the change in watts based on the change in decibels:

10^(-11.48/10) = .07 watts required. I personally will multiply this wattage figure by ten to cover hidden peaks not registered by my meter. My answer is .7 watts. Some will want a headroom of 100 times the power. Then the answer would be 7 watts. By the way, 10 times the power = a 10 decibel increase - and 100 times the power equals a 20 decibel increase.

Example 2, if owning an 80 wpc receiver, at what SPL decibel level can it be played before it goes into distortion? In this example, speaker sensitivity is 95 db at 1 meter and sitting 12 feet from each speaker:

10 x log (3.28/12)² = -11.27 db for speaker distance. 95 - 11.27 (distance) + 6 (stereo + room) = 89.73 db at one watt. The extra decibels from 80 wpc = 10 x log (80/1) = +19.03 db. 89.73 + 19.03 - 10 (headroom adjustment for peaks not measured) = 98.76 decibels.

This is assuming that EVERYTHING ELSE IS EVEN. Trouble is, it never is with amps.

Walt

[bootman]

Nov 11, 2017 13:24:12 GMT -5 leonski said:

Movie theaters are apparently set up for 85db with 20db peaks. For a 90" to 120" movie? You should be OK, right?

So use that calculator to determine how much power you would need to make sure those 20dB peaks happen with minimal distortion.
Lets just assume it takes 10 Watts to get 85dB from 80-20kHz at 3 meters from the speakers.

[leonski]

Nov 12, 2017 7:27:29 GMT -5 bitsandbytes said:

Another good formula is for the apparent or perceived listening volume. A 10 decibel increase is required to get twice the perceived volume. That formula would be:

2^{(decibel change/10)}

An example is if trying to decide between a 110 wpc - or the same brand of amp with 170 wpc. Using the previously mentioned formula, need to calculate decibels first:

10 x log (watts/base reference in watts) = 10 x log (170/110) = 1.89 decibels increase

2^(1.89/10) = 2^.189 = 1.3997 = perceived listening volume increase of 14%. Meaning the 170 wpc amp will sound 14% louder before going into distortion than the 110 wpc amp.

The inverse square formula is used for calculating decibels lost with speaker distance. The sensitivity rating of speakers is taken with one speaker in an anechoic (non-reflective) chamber either 1 meter or 3 feet from the speaker. This formula:

10 x log [(3.28/measured distance in feet)²] Note: This 3.28 is with the sensitivity given at one meter with a one watt output. If taken at 3 feet, then the 3 is used instead of 3.28. Example, if sitting 8'8" from each speaker with the speaker sensitivity given at one meter, then:

10 x log (3.28/8.67)² = 10 x log .378² = 10 x log .143 = -8.45 db. The actual calculation without rounding off each step would be -8.4429 decibels.

Calculating the change in watts based on the change in decibels yields:

10(^{decibel change/10)}

This is useful when trying to figure out the watts required to achieve a certain level in decibels.

As only one speaker is used in sensitivity ratings, the second speaker has to be added. 10 x log (2/1) = 3.01 decibels increase. The room itself adds to the sound level. Paradigm uses a 3 db addition to differentiate between a live room and their anechoic chamber. This decibel increase will be different dependent upon room size, the hard and soft surfaces, windows, hollow doorways, openings to other rooms, and the broadband absorption and diffusion used. These will widely vary at each frequency too. For simplicity, will add +6 db for stereo and room adjustment.

An example putting this all together. If sitting 8 feet from the speakers with a speaker sensitivity of 90 decibels measured from 3 feet away, just how much power would be required to measure peaks on a SPL meter of 75 decibels?

10 x log (3/8)² = -8.52 db for distance. 89 - 8.52 (distance) + 6 db (room + stereo) = 86.48 decibels at one watt at the listening position. With 75 db required, this is a change of -11.48 decibels required. Using the formula to calculate the change in watts based on the change in decibels:

10^(-11.48/10) = .07 watts required. I personally will multiply this wattage figure by ten to cover hidden peaks not registered by my meter. My answer is .7 watts. Some will want a headroom of 100 times the power. Then the answer would be 7 watts. By the way, 10 times the power = a 10 decibel increase - and 100 times the power equals a 20 decibel increase.

Example 2, if owning an 80 wpc receiver, at what SPL decibel level can it be played before it goes into distortion? In this example, speaker sensitivity is 95 db at 1 meter and sitting 12 feet from each speaker:

10 x log (3.28/12)² = -11.27 db for speaker distance. 95 - 11.27 (distance) + 6 (stereo + room) = 89.73 db at one watt. The extra decibels from 80 wpc = 10 x log (80/1) = +19.03 db. 89.73 + 19.03 - 10 (headroom adjustment for peaks not measured) = 98.76 decibels.

This is assuming that EVERYTHING ELSE IS EVEN. Trouble is, it never is with amps.

Walt

You make the 'everything else is even' proviso.    And also note it NEVER is!      How Very Very True.        Which leads me to my first question:
When choosing an HT amp, would you Really choose based on a 1.9db increase in power?    When nobody had any real idea how well EITHER amp did into a real speaker load?  

Care must be taken with calculating speaker levels at distance.    1 meter fairly safely gets the room out of the picture, if it's a normal room.    But by the time you are back 3 or maybe 4 meters, room gain starts to get involved and it can be difficult to simply 'name a value' of increase or rather lessening of decrease in level.   

The other factor to be considered the the RT60 of any room.   That is the amount of time required for a 'impulse' to decay by 60db.     This is kind of a measure of 'liveness' of a room and may be related in some fashion back to room gain.   

[bitsandbytes]

Nov 12, 2017 14:34:08 GMT -5 leonski said:

You make the 'everything else is even' proviso.    And also note it NEVER is!      How Very Very True.        Which leads me to my first question:
When choosing an HT amp, would you Really choose based on a 1.9db increase in power?    When nobody had any real idea how well EITHER amp did into a real speaker load?  

Care must be taken with calculating speaker levels at distance.    1 meter fairly safely gets the room out of the picture, if it's a normal room.    But by the time you are back 3 or maybe 4 meters, room gain starts to get involved and it can be difficult to simply 'name a value' of increase or rather lessening of decrease in level.   

The other factor to be considered the the RT60 of any room.   That is the amount of time required for a 'impulse' to decay by 60db.     This is kind of a measure of 'liveness' of a room and may be related in some fashion back to room gain.   

In answer to your question, no, a decibel increase (nor decrease) has no bearing on which amp I would choose to buy. The watts per channel is irrelevant to me. The only consideration is how it (or they) sound with my speakers in my room to my ears.

You are absolutely correct about the impact of the room affecting the inverse square formula for decibel loss. That 3 db gain for the room is a HUGE oversimplification. By the way, using the inverse square formula to calculate RT60 with regards ONLY to distance between one speaker and the listener is:

10 x log (3/3000 feet)² = -60

Of course, with absorption, wave cancellation and scattering going on in a real life room reducing the decibel levels, the footage would measure much lower. It does however demonstrate how important the room's reflections are  in regards to volume.

Walt

[leonski]

Thanks for clarification:

Yes, Indeed. Sound is 'king'. That's why testing is so important in YOUR room / system.

All this math and the large number of considerations in HT or even stereo room design is how a few companies make a good living doing setup and design of such spaces.

I know what I'd like to do, but I'm not wealthy enough to afford a custom room with non-parallel walls, double hung sheetrock on 2 adjacent walls, built in sound absorption material and
at least 4 exclusive circuits, from a dedicated 'box'. Not to mention offset studs in-wall, double 'airlock' door to the rest of the house and countless other features and details.
The worst? Trying to find someone who KNEW what I wanted and could actually build it.

[405x5]

This thread MAY come in handy....been contemplating becoming a private contractor for commercial space travel!

[leonski]

You don't have far to go!

[leonski]

Here is the real formula, for RT60 accepted since late 1800s, no less.

www.sengpielaudio.com/calculator-RT60.htm

This formula deals with reverberation and is maybe a reflection of how 'live' the music is, to a listener.

Don't forget, the characteristics of YOUR room are 'added' to the recorded characteristics for a 'final' presentation.

A dead room with a dead recording studio with no reverb or sweetners will produce a very sterile recording, probably.

[leonski]

While not strictly a 'Calculator' this IS a real aid to room setup and arrangement.

I've used sketchup for years to 'envision' an idea and in some cases even design furniture.

www.sketchup.com

I use the free version and have never updated. Be warned of SOME learning curve and maybe what you'd think of as 'odd' behavior, but working WITH the program you can make very nice drawings, indeed.

[DavidR]

[405x5]

Nov 17, 2017 1:46:51 GMT -5 DavidR said:

By my calculations, this thread will go belly up within the hour.....(with any luck at all)

[leonski]

Thanks, 405, I knew I could count on your support.

[leonski]

For those FEW curious about surge suppression and power conditioners:

www.rapidtables.com/calc/electric/Joule_to_Watt_Calculator.htm

This calculator will give you watts' of energy when inputting Joules and TIME.

Might be useful if you have a surge suppressor which you think has lost function.
Run some numbers and see if anything makes sense.   If you've had a lightning strike 
or other large surge?    MIght be time to consider a new suppressor.

[leonski]

amcoustics.com/tools/amroc?l=23&w=13&h=8&ft=true&r60=0.6

Over in the Def Tech Thread I promised to link a room mode calculator. This is a pretty dense bit of code, but can be waded thru.
Other, simpler sites exist with better or simply easier to understand graphics and charts.

OR?

www.bobgolds.com/Mode/RoomModes.htm


In these calculators 'mode' refers to how many BOUNCES the sound takes. In a cubic room of 8 sides, you can have multiple modes of 'bouce', each which produces its 'spectrum' of frequencies.

[Jean Genie]

Nov 11, 2017 23:14:18 GMT -5 leonski said:

www.mcsquared.com/wavelength.htm

Another potentially useful calculator. This one allows a frequency to wavelength conversion.

This kind of information is useful in designing listening areas. Speaker designers use it in baffle design and enclosure proportioning.

www.mcsquared.com/modecalc.htm

The ROOM MODE CALCULATOR is useful for deign and execution of listening rooms. Checking in advance for Standing Waves allows for the construction of rooms with fewer problems and less need of Room Treatments (not to the exclusion of such treatments, however)
Entering square floor plans shows why square rooms and rooms with dimensions that are multiples of one another should be avoided. Even a room with an 8 foot ceiling which is 16x24 will probably give problems.

So I entered my room dimensions into The ROOM MODE CALCULATOR and was rewarded with this gibberish:

Room Dimensions
Room length

22.5
Feet

Room width

14.5
Feet

Room height

6.5
Feet


Axial Room Modes
Axial room modes

25.11111111111111
Hz
38.96551724137931
Hz
86.92307692307693
Hz
50.22222222222222
Hz
77.93103448275862
Hz
173.84615384615387
Hz

75.33333333333333
Hz
116.89655172413794
Hz
260.7692307692308
Hz
100.44444444444444
Hz
155.86206896551724
Hz
347.69230769230774
Hz

125.55555555555554
Hz
194.82758620689657
Hz
434.61538461538464
Hz
150.66666666666666
Hz
233.79310344827587
Hz
521.5384615384615
Hz

175.77777777777777
Hz
272.7586206896552
Hz
608.4615384615385
Hz
200.88888888888889
Hz
311.7241379310345
Hz
695.3846153846155
Hz

226
Hz
350.6896551724138
Hz
782.3076923076923
Hz
Tangential Room Modes
Tangential room modes have 1/2 of the energy of axial modes (-3dB). 

Tangential Room modes

46.35600754080096
Hz
90.47756187591328
Hz
95.25719309145833
Hz
92.71201508160192
Hz
180.95512375182656
Hz
190.51438618291667
Hz

139.0680226224029
Hz
271.43268562773983
Hz
285.77157927437503
Hz
185.42403016320384
Hz
361.9102475036531
Hz
381.02877236583333
Hz

231.78003770400485
Hz
452.3878093795664
Hz
476.28596545729164
Hz
278.1360452448058
Hz
542.8653712554797
Hz
571.5431585487501
Hz

324.4920527856068
Hz
633.342933131393
Hz
666.8003516402083
Hz
370.8480603264077
Hz
723.8204950073062
Hz
762.0575447316667
Hz

417.2040678672087
Hz
814.2980568832194
Hz
857.3147378231249
Hz
Oblique Room Modes
Oblique room modes have 1/4 of the energy of axial modes (-6dB). 

Oblique room modes

98.5114243978735
Hz
197.022848795747
Hz
295.5342731936205
Hz
394.045697591494
Hz
492.55712198936743
Hz
591.068546387241
Hz

689.5799707851145
Hz
788.091395182988
Hz
886.6028195808614
Hz
Sooo... as a less informed layman, how am I supposed to interpret this?😕🙉