As if through a glass darkly.

Imagine, if you will, that you wish to measure the volume of a space for your infinite baffle enclosure to which there is no reasonable, physical access. It might be an underfloor crawl space for example. Access is poor without making a rather large hole in the floor. Even if you don't lose a cat, baby or child down there any sensible partner is going to reach for their coat. Or yours!

Meanwhile, you suffer from claustrophobia and don't own a long enough tape measure anyway. Without somebody holding the other end tightly you cannot be certain that the far end of the tape hasn't followed you. As you dragged yourself along on your belly, with a torch in your teeth,  letting out your tape until you finally hit something solid. Do you return by the same arduous route to check if the tape has moved?

I was inspired to examine a similar measurement problem by the discovery of an old, disused and rather neglected farmhouse. Which we had found for sale while on an outing in the car rather a long way from home. Arranged on only one floor and well over twenty yards/metres long the old house seemed to have as many windows as an early railway carriage. The many rooms ran in a parallel series along a central, dividing wall. So there was no clear view through the property from one side to the other. The old house simply oozed character but badly needed some skilled and expensive TLC.

For some reason I became fascinated by the problem of how any interested party would be able to measure the various rooms without gaining access to the indoors. Would my fantasy farmhouse purchase offer any rooms as obvious candidates for a Home Theatre or music room? Well, one can dream!

Once inside it would be quite easy to rough out a sketch and measure the dimensions of all or some of the many rooms. Locked outside, but with easy access to every exterior window, made it a far more interesting challenge. How could I have checked the room sizes?

The answer to the measurement  puzzle was, of course, a builder's laser range finder. These devices often have a number of preprogrammed tricks to aid us. Though a smidgen of simple geometry might also be needed. Pythagoras had obvious mulled over this same problem too and provided a simple and elegant solution. No doubt he used a long cane marked at intervals instead of a laser. Though you never know.

Let us assume that you have visual access to the interior of a room or other space. Such that you can see the entire width of the opposite wall if you only want to know the floor dimensions and area. If you want volumes or wall surface area then you will need a view of the opposite wall from floor to ceiling. Though some lasers can calculate dimensions indirectly from direct measurements.

Window glass need not be a hindrance to our measurements. Not even double/thermal glazing. Nor need you worry, too much, about the size of your viewing aperture or window. In fact the smaller the better if it helps to increase the accuracy of your laser measuring position. It also helps the accuracy of your results if you have a laser device which can have the reference measuring surface moved to its front edge. This is usually just a matter of pressing a particular button on most of these devices.

Start by taking a simple distance measurement to the opposite wall. Just make sure the spot has hit a normal bit of wall and not a window, jutting fireplace or a recess. Make sure you keep the laser square (perpendicular) to the opposite wall. We'll call this first measurement D for Depth and write it down.

Now we will mentally divide the width of the opposite wall into two lengths A and B. Their dividing point is where you measured D directly opposite your viewpoint. Your viewpoint does not even need to be in the middle of the room. Measure the distance to the far corners at the same height as your viewpoint and make a note of each measurement. These two measurements are your hypotenuses for two, right angled triangles. Hypotenuse just means the longest side of a triangle. You can call these measurements L1 and L2. Or any other name which help you avoid confusion.

If you square each measured hypotenuse in turn and then subtract the square of  D from each you will have two more figures to write down. Squaring just means multiplying a number by itself.

First half wall:
L1 x L1 - D x D = AxA.
Or L1^2 - D^2 =  A^2
(Both mean the same thing)

Second half wall:
L2 x L2 - D x D = B x B.
Or L2^2 - D^2 =  B^2.

Use a calculator, or multiply each number longhand, by itself, to obtain its square. Now you probably do need a calculator to take the square root of each resulting number A^2 and B^2 .

The square root of each will, in turn, give you the widths of the two halves of the opposite wall. A and B. Now just add these two numbers together and you have the full width of the opposite wall.

If you doubt your calculations then try using 3, 4, 5 triangle as your working example. By a very happy coincidence a triangle with sides of 3, 4 and 5 units forms a perfect right angle between the two shorter sides. The 3, 4 5 triangle is much used in building work in the absence of a precision builder's square or laser alignment tools. BTW:You can use any units you like as long as they all the same: 3, 4, 5 feet. 3, 4 , 5 yards or 3, 4 , 5 miles, leagues, meters, chains, nautical miles, light years, parsecs, AU or furlongs. Just don't mix your measurement units.

Back to our real world measurements:  If you multiply the full width by your first measurement D you will have the area of the floor. So you can order a new carpet, tiles, vinyl or lino without ever standing in that room.

You can use the same system for measuring the height of the inaccessible room assuming you can see the far wall from floor to ceiling. Some of the better laser range finders can do this calculation for you indirectly. Simply by taking distance readings from both the top and the bottom of the wall in a pre-selected mode.

Or just divide the height of the wall into two and use Pythagoras just as we did in the width calculation. Except that your two right-angled triangles will be stacked one above the other. With their adjacent sides level with your viewpoint.

You can now calculate the area of each end wall of the room. D x H.
Or the area of each long wall. A + B x H.
Or the volume of the room using the Width x Height x Depth.

An underfloor IB space (enclosure) can be just as easily measured using a laser range finder without physically entering the space. All you need is a clear enough view to point the laser and measure the full width and full depth of the space. Then measure the height and multiply the three numbers together to obtain the volume of the crawl space. Never assume that a crawl space is the entire visible floor area of a room or even your entire home. It is always best to measure it to see if it provides a suitable Total Vas multiplier of at least 5.

The same method can be applied if you forget the volume of the space behind your infinite baffle wall but can no longer access it yourself. Though a suitable hatch or door is useful for maintenance. Or adding sound absorbing, insulation material. Just don't use the access as an excuse for using the space for storage. Not unless you have plenty of room to start with.

No doors, floors, windows or tape measures were hurt in the creation of this post.