Note: Observe 555 minimum and maximum R/C values (

Test example: Assume the inductor has negligible resistance and that upon carrying out the procedure described in the above-referenced page, the frequency that resulted in a half-amplitude reading was 1,175,000 Hz (enter values in Hz, not KHz or MHz). Entering this value in the frequency box below without commas (leave the resistance box empty) results in an inductance measure of 3.9 μH, which happens to be the value that the inductor in question should have had.

If the inductor has a significant internal resistance (can be measured with an ohmmeter) then enter this value in the resistance box before clicking ‘compute.’

Note: The experimental method is fully described at the page linked in the introductory paragraph above.

Select units for inductance.

The formula reproduced above includes an exponential term, so the inverse must necessarily contain a logarithm—I thought this as good as reason as any to refresh my fading memory of logarithms. A detailed derivation entails several steps, but can be satisfactorily summarized in two. The first is the direct or immediate inverse of the formula for diameter, while the second substitutes the natural logarithm for log base 92, and combines constants in order to simplify the resulting expression.

Formula (3), giving AWG as a function of diameter in millimeters, has excess precision—more than the original formula. However, the calculator (below) rounds the answer to the nearest whole number (i.e., wire gauge number).

Here is another backwards calculation. This one is more a mental exercise—It doesn’t really merit a calculator, but just for fun. Many sources (for example, Wikipedia) give the following formula for VSWR in terms of reflected power (or, more precisely, the ratio of reflected to forward power):

Assume that the ratio of reflected to forward power is a positive fraction less than 1. The question is: “For a given VSWR, what proportion of the power is reflected?” As I said, this is normally a mental calculation, unless VSWR is extremely high, in which case it is probably too late to have asked the question! First, simplify the formula with a substitution:

Use ordinary algebra to solve for Γ and then square both sides.

An example will demonstrate how easy it is to calculate reflected power from VSWR. Suppose VSWR is 3:1. 3 minus 1 is 2. 3 plus 1 is 4. 2/4 = 1/2 and (1/2)

Convert Decimal to Fraction: Expressing a fraction as a decimal number is easy—simply divide the numerator by the denominator. However, the reverse problem, to express a decimal number as a fraction to an acceptable approximation, is less obvious. To clarify the context, this discussion is about converting ordinary (short) decimal numbers, such as arise in everyday experience, to simple fractions. In the United States, tools such as wrenches and drill bits and so forth are specified in inches or fractions of an inch. Thus a digital caliper may display an inch measure in fractional form for the convenience of selecting the correct tool. (Metric measurement does not suffer this encumbrance.) The particular situation that brought the decimal to fraction problem to my attention had nothing to do with SAE (stands for the Society of Automotive Engineers), and will be described below, but first I will explain the calculation itself.

Any finite decimal number is easily converted to a fraction by putting the decimal digits in the numerator and a corresponding power of 10 in the denominator, but that is not quite satisfactory. Generally, a shorter fraction would be preferred, if there is one. As it happens, there is a systematic procedure for converting a decimal number into what is called a continued fraction, by breaking the given decimal into an integer part and reciprocal of the remainder, then iterating the process. At each term, one can compute a rational fraction represented by the continued fraction up to that term. Such fractions successively approximate the decimal number.

Example: 0.367431640625

From the illustrated example, it seems obvious how to decide where to stop iterating. Evaluate the fraction at each term, compare to the decimal number, and decide whether the fraction satisfies the desired precision. In the JavaScript calculator below, precision is equal to the length of the input decimal plus one place. The idea is for the fraction to equal the original number up to its length, without a large digit in the next position. For greater precision simply add zeros to the end of the decimal. The following paragraphs describe the exercise that led to programming this calculator.

Si5351 A/B/C Programmable Clock Generator The Si5351* must be one of the most popular chip families in ham radio. This Silicon Labs clock generator is found in at least four devices that I own, including a couple of QRP transceiver kits and the NanoVNA (vector network analyzer). An Si5351 breakout board, such as the one pictured on the left, invites experimentation with an Arduino or other development kit that can communicate with the clock generator via i2c. The device has two PLL’s labeled A and B, and three outputs labeled CLK0, CLK1, and CLK2. Parameters that determine clock outputs are called a ‘frequency plan’. A desktop computer application from Silicon Labs called ‘ClockBuilder’ can be used to assist in computing frequency plans.

To order to learn a little about Si5351 programming I set about to produce a range of test frequencies as clock outputs. This exercise led to the problem of converting a decimal number to a fraction. To explain, the Adafruit Si5351 library for Arduino includes the methods setupPLL(...) and setupMultisynth(...). Suppose we have a base frequency and target frequency in mind, and have computed the ratio of these frequencies as a decimal number.. To argue a frequency multiplier or divider to one of these library functions it is necessary to express the decimal part of the ratio as a fraction (i.e., as integer numerator and integer denominator). The fraction might be as simple as 0/1 or 1/2, but in some cases it is less trivial. I should stress that this problem does NOT arise in the context of developing a frequency plan with the aid of the Silicon Labs ClockBuilder application. It pops up where you want to change an output frequency by fiddling either the multisynch or feedback divider, leaving the other fixed. This is something that I played with, in learning about the Si5351.

You are given a principal loan amount (P), an
interest rate (i), and a number of equal payments (N). Interest is
expressed as a fraction or proportion per payment. For
example, if the loan is to be paid monthly and the interest is 6% per
year, fractional interest would be 6÷1200 or .005. The divisor
1200 reflects conversion from percent to fraction (÷100) and from
annual to monthly (÷12). The number of payments (N) refers to the total
number over the course of the loan. For example, if payments
are monthly and the loan is for 6 years, N = 6×12 = 72. Let A stand for
the equal payment amount:

Many years ago (i.e., before Internet and before personal computers) a calculator salesman asked me to program this problem for his machine, and promised a case of scotch whiskey as payment. I never saw a drop of scotch, but working out a program for the problem was reward enough. Back then it wasn’t JavaScript!

Example: Suppose you wish to borrow $25,000.00 at an annual periodic rate of 6%, and make monthly payments for 6 years. Enter 25000 as a number into the first box (omit the dollar sign and commas), .005 in the second box (see first paragraph above), and 72 in the third box. Then click the ‘Compute Amount’ button. For these input values the monthly payment should be $414.32. This amount consists purely of principal and interest. It does not include any add-on charges that may be included in a real loan, such as taxes, insurance, and so forth.

The author makes no claim as to the accuracy or completeness of information presented on this page. In no event will the author be liable for any damages, lost effort, inability to reproduce a claimed result, or anything else relating to a decision to use the calculators or supplemental information on this page.