The formula, and the one input you cannot guess
Tension in pounds is approximately (UW x (2 x L x F) squared) divided by 386.4, where UW is the unit weight of the string in pounds per inch, L is the scale length in inches and F is the frequency in hertz. The 386.4 is the acceleration of gravity in inches per second squared, present because the formula converts a mass figure expressed as weight into a force.
Three of those four inputs you know. Scale length is on the instrument, frequency comes from the tuning, and gauge is on the packet. Unit weight is the one you cannot look at a string and determine, because it depends on how the string is built. A plain steel string is a solid cylinder and its unit weight follows directly from its diameter and the density of steel, so estimating it is safe. A wound string is a core wire with a wrap around it, and two strings of identical outside diameter can differ by ten percent or more in weight depending on the core diameter, the wrap material and how tightly it is wound. That is why unit weight is a manufacturer figure and why this page lets you type it in. Every string maker publishes a table of them.
The estimates used when you do not supply one are 0.2238 times the gauge squared for plain steel and 0.178 times the gauge squared for wound, both in pounds per inch with the gauge in inches. The plain figure is accurate to about one percent. The wound figure is a fitted average and can be several percent out on any particular string.
Why tension goes with the square of the frequency
The frequency term is squared, which is the single most useful thing to know about this formula. Drop a string a whole tone and its frequency falls to about 0.891 of what it was, so its tension falls to 0.891 squared, which is 0.794. That is a loss of roughly 21 percent. Drop it a full fourth and you keep about 56 percent of the tension.
Gauge enters through unit weight, which goes with the square of the diameter. So going from a .046 to a .052 raises unit weight by (52/46) squared, about 1.28, and raises tension by the same factor if the pitch is unchanged. Put those together and the drop-tuning arithmetic becomes concrete: two semitones down costs you 21 percent, and recovering it needs a gauge about 12 percent larger, since 1.12 squared is roughly 1.25.
| Change | Effect on tension |
|---|---|
| Down one semitone | About 11% less |
| Down a whole tone | About 21% less |
| Down a minor third | About 29% less |
| Gauge up 10% | About 21% more |
| Scale length up 1 inch from 24.75 | About 8% more at the same pitch |
Heavier in a lower tuning is not automatically tighter
This is the thing the calculator exists to settle. A .046 at E2 on a 25.5 inch scale is around 17.7 pounds with a typical wound unit weight. Drop that same string to D2 and it falls to about 14.1. To get back to 17.7 at D2 you need a unit weight about 25 percent higher, which is a gauge in the .051 to .052 region. A .048 gets you to roughly 15.4, which is still noticeably slacker than where you started, even though the packet is heavier and the tuning is lower.
So the answer to whether the heavy set in drop tuning is tighter than the light set in standard is: sometimes, and you have to do the arithmetic. Sets sold for drop tunings usually make the bottom string much heavier and leave the top three nearly alone, which is deliberate, because most people only drop the bottom string and want the treble strings to feel unchanged. If you are dropping the whole instrument, that set will feel unbalanced.
Scale length changes everything about the feel
Scale length appears squared too. At the same pitch and gauge, a 25.5 inch scale carries about 6 percent more tension than a 24.75 inch scale, which is why the same string set feels stiffer on a longer-scale instrument and why bends take more effort. The effect is much larger between bass scales: a 34 inch scale carries roughly 28 percent more tension than a 30 inch scale for the same string and pitch, which is the main reason short-scale basses feel floppy on the low string and are often sold with heavier sets.
Measure your own scale length rather than trusting the specification. The usable figure is twice the distance from the nut to the centre of the twelfth fret, which is exact by construction. The nut-to-saddle distance is longer than that by the compensation amount and varies string to string, so it is the wrong number to use here.
Total tension and what it does to the instrument
The total across a set is what the neck and top are actually holding, and it moves with everything above. A light electric set on a 25.5 inch scale lands somewhere around 90 to 100 pounds; heavier sets and acoustic sets go well past that. Changing sets meaningfully changes the load, which changes the relief in the neck and, on an acoustic, the load on the top and bridge.
Treat every figure on this page as a starting point to be measured, not a specification. What governs is the string maker unit weight and what the instrument was built to carry. An instrument set up for one tension will usually need the truss rod and the action revisited after a large change, and some instruments should not be taken far from what they were designed for at all. If you are unsure, that is a question for whoever set it up.
Where this connects
The frequencies used here come from equal temperament, which the note frequency calculator covers along with cents and reference pitch. If you are working on the instrument rather than the strings, the fret position calculator handles fret spacing and the compensation question that this page deliberately leaves out. For playing to a tempo while you evaluate a new set, the metronome is there.
Questions people ask
What string gauge do I need for drop tuning?
Work backwards from the tension you already like. Calculate the tension of your current set at standard pitch, then use the same page to try gauges at the new pitch until the numbers match. As a rough guide, recovering the tension lost to a whole step down needs a gauge about 12 percent larger, and a minor third down needs about 18 percent larger. If you are only dropping the bottom string, only that string needs to change. If you are dropping everything, everything does, or the set will feel lopsided.
Why does the calculator ask for unit weight instead of working it out from the gauge?
Because for wound strings it cannot be worked out from the gauge with any accuracy. A wound string is a core with a wrap, and manufacturers make very different choices about the ratio between the two. Two strings with the same outside diameter can differ by ten percent or more in weight per inch, which shows up directly in the tension. Plain strings are solid steel and the estimate is fine. For wound strings, get the unit weight from the maker of the strings you actually own and enter it, or treat the result as a comparison between options rather than a measurement.
Is higher tension better?
No, it is a preference with trade-offs on both sides. Higher tension resists bending, gives a firmer attack, is less likely to buzz against the frets when dug into, and holds pitch better under a heavy pick. Lower tension bends more easily, is kinder on the hands over a long session, and often sounds looser and warmer. The failure modes sit at the extremes: too low and the string rattles and goes sharp when you fret it, too high and the instrument fights you and carries a load it may not have been built for. Most people find a range they like and then keep the tension roughly constant across tunings by changing gauges.
Does changing string gauge require a setup?
A meaningful change, yes. The strings are the load holding the neck against the truss rod, so a large change in total tension changes the relief. Higher tension pulls more relief into the neck, lower tension lets it straighten, and either way the action and the intonation move with it. A small change of one gauge step is often survivable without touching anything; a jump of several steps or a whole-instrument retune usually is not. Nut slot width also becomes a problem if you go much heavier, since a slot cut for a .009 will pinch a .011 and cause tuning instability.
Why is my calculated tension different from the manufacturer chart?
Almost always the unit weight. Enter the maker figure for the exact string and the numbers converge closely. The other difference is scale length: charts are usually quoted at one nominal scale, commonly 25.5 inches for guitar or 34 for bass, and your instrument may not be that. There is also a small real-world gap because the speaking length after saddle compensation is slightly longer than the nominal scale, so measured tension runs a little above the calculated figure. None of these change the comparisons between options, which is what the page is actually good for.