This guitar string tension calculator evaluates one published relation. Given a string’s unit weight, the vibrating length it is stretched over and the frequency you want it to sound, there is exactly one tension that satisfies the physics, and the formula that returns it is the one string manufacturers use themselves. The tool applies it, states the units convention it uses, and shows what happens when you change the pitch or the scale length.
The reason most string tension pages are unreliable is that they bury a unit weight table inside the code. Unit weight is a property of a specific product — core diameter, wrap material, wrap diameter and construction all change it — so a table that is not the maker’s own table is a guess dressed up as data. Arb Digital takes it as an input instead, points you at where the real figure is published, and does the arithmetic honestly on whatever you supply.
What This Calculator Does
It returns the static tension of one string in pounds, newtons and kilogram-force. It converts a note name into a frequency using twelve-tone equal temperament against an adjustable A4 reference, so you can work in either notes or hertz. It shows the same string’s tension on a second scale length, which is the honest way to answer “what will this set feel like on my other guitar”. And it plots tension across a range of semitone shifts, because the square-law relationship between pitch and tension is the single most useful thing on this page.
What it does not do is tell you what set to buy, or state a tension that is correct for an instrument. Neck relief, truss rod range, top bracing on an acoustic and the instrument’s own history all bear on what a given total tension does to a particular guitar, and none of that is in the formula. The fret spacing calculator covers neck geometry, which is a separate question from tension entirely.
How to Use It
- Get the unit weight from your string maker. Tension charts published by string manufacturers list it per product code. Do not use a figure from a forum post.
- Measure your scale length from nut to bridge saddle, or measure nut to twelfth fret and double it.
- Set the pitch either by note and octave or directly in hertz, and adjust the A4 reference if you tune to something other than 440.
- Enter a second scale length to see the same string on another instrument at the same pitch.
- Read the semitone bars before you commit to a drop or raised tuning, because that is where the surprises are.
The Formula and Its Units Convention
The relation is the one D’Addario publishes in its own string tension resource:
T = (UW × (2 × L × F)²) ÷ 386.4
where T is tension in pounds, UW is unit weight in pounds per linear inch, L is scale length in inches and F is frequency in hertz. The 386.4 is gravitational acceleration expressed in inches per second squared, which is what converts a weight-based unit weight into a mass. The convention is entirely imperial, and mixing a metric unit weight into it without converting is the most common way to get a wrong answer. This tool converts grams per metre to pounds per inch internally at 17,857.9673 grams per metre to one pound per inch, and millimetres to inches at 25.4, before the formula is ever evaluated. D’Addario also notes the conversion from the result to newtons: multiply by about 4.45.
Underneath, this is the standard result for a vibrating string, described in the University of New South Wales physics notes on strings, standing waves and harmonics: the fundamental frequency is one over twice the length, times the square root of tension over linear mass density. Rearranged for tension and expressed in the imperial units string makers use, it becomes the formula above.
Worked check with this page’s defaults. A unit weight of 0.000032 lb/in on a 25.5 inch scale, tuned to E4, which is 329.6276 Hz at A4 = 440 in equal temperament. Then 2 × 25.5 × 329.6276 = 16,811.0 and squared that is 2.8261 × 10⁸. Multiply by 0.000032 to get 9,043.5, divide by 386.4, and the tension is 23.40 lb. That is 104.11 newtons and 10.62 kgf. The same string at the same pitch on a 24.75 inch scale returns 22.05 lb — three per cent lighter for a three per cent shorter scale, because at fixed pitch tension goes with the square of length while frequency goes with its inverse.
Why the Square Law Is the Whole Story
Tension is proportional to unit weight to the first power and to frequency to the second. That asymmetry drives almost every practical decision. Going up one semitone multiplies frequency by the twelfth root of two, about 1.0595, so it multiplies tension by the sixth root of two, about 1.1225 — a 12.2 per cent jump for one fret of pitch. Two semitones is very nearly 26 per cent. Using this page’s defaults, that same string goes from 23.40 lb at E4 to 29.49 lb at F#4, and down to 18.58 lb at D4.
Unit weight, by contrast, is linear. Moving from a .012 to a .013 plain string raises unit weight by roughly the ratio of the squared diameters, so tension moves by a similar proportion, and in practice that is a smaller change than a single semitone of tuning. This is why players who drop-tune a set and complain of floppiness are usually under-correcting: matching the old tension after a two-semitone drop needs about a 26 per cent heavier string, which is more than one gauge step.
The same logic explains baritone instruments. A longer scale at a lower pitch can land at ordinary tension, because the length increase compensates for the pitch decrease. Working out that trade-off is exactly what the second scale length field is for.
Plain Strings, Wound Strings and Why Diameter Is Not Enough
For a plain steel string, unit weight follows directly from diameter and density, so gauge alone almost determines it. For a wound string it does not. A .046 wound string has a core, a wrap and an amount of air, and its unit weight depends on how those are proportioned. Two makers can both sell a .046 nickel-wound string with meaningfully different unit weights and therefore different tension at the same pitch. Hex core and round core differ. Nickel-plated steel, pure nickel, phosphor bronze and stainless steel all differ in density.
This is the practical reason the tool refuses to hold a table. A gauge number is not a unit weight, and any page that maps one to the other is implicitly assuming a single manufacturer’s construction. The published tension chart for the strings you actually intend to buy is the only source that answers the question you are asking.
What Total Set Tension Does and Does Not Tell You
Add the six computed tensions and you get the total pull the set exerts on the instrument, which for a common electric set on a 25.5 inch scale lands somewhere in the region of 100 lb. It is a useful number for comparing two sets on the same instrument, and a poor number for comparing across instruments. An archtop with a floating bridge, a solid body with a fixed bridge and a flat-top acoustic with a braced top respond to the same total load completely differently.
Total tension also governs a floating tremolo. Change the set and the spring balance changes, so the bridge sits at a different angle and every string goes out of tune with every other. Calculating the new total before you restring tells you how much spring adjustment to expect. The tension force calculator handles the general statics of a loaded line, and the force converter is there when a maker publishes in one unit and you think in another.
Arb Digital builds calculators that state their source, their units and their limits. Browse the library, or tell us which page your audience keeps bouncing off.
Browse Free Tools Talk To Arb DigitalCommon Mistakes to Avoid
- Mixing units. The published formula is imperial throughout. A metric unit weight or a scale length in millimetres has to be converted first, which this tool does explicitly.
- Using gauge as a stand-in for unit weight. It works approximately for plain strings and not at all for wound ones.
- Measuring the neck instead of the scale. Scale length is nut to bridge saddle. Nut to twelfth fret, doubled, is the reliable shortcut.
- Forgetting the A4 reference. Tuning to 432 or 415 shifts every frequency and therefore every tension, and the shift is not negligible.
- Reading tension as a verdict on the instrument. Whether a neck, top or bridge tolerates a given total load is a question for a luthier, not a formula.
Related Free Tools From Arb Digital
Work out where the frets go with the fret spacing calculator, convert a single pitch and read its cents deviation with the note frequency converter, explore what sits above a fundamental with the harmonic series calculator, handle the general loaded-line case with the tension force calculator, switch units with the force converter, and get a feel for the underlying wave relation with the wavelength calculator. Everything else is in the free online tools hub.
Frequently Asked Questions
The published relation T = (UW multiplied by the square of 2 times L times F) divided by 386.4, with tension in pounds, unit weight in pounds per linear inch, scale length in inches and frequency in hertz. It is the formula D’Addario sets out in its own string tension resource, and it is the standard vibrating-string result expressed in imperial units.
Because unit weight belongs to a specific product, not to a gauge. Core and wrap construction, wrap material and density all change it, so two makers can sell the same nominal gauge with different unit weights. String makers publish the figure in their tension charts, and using theirs is the only way to get an answer about the strings you will actually fit.
A great deal, because tension goes with the square of frequency. One semitone is a factor of about 1.1225, so roughly 12 per cent, and two semitones is close to 26 per cent. Matching your old tension after a two-semitone drop takes more than a single gauge step of extra weight.
Yes. At fixed pitch and fixed string, tension is proportional to the square of the scale length. A 24.75 inch scale carries about three per cent less tension than a 25.5 inch scale for the same string at the same note, which is why the second scale length field is there.
Gravitational acceleration expressed in inches per second squared. It converts the weight-based unit weight the imperial convention uses into the mass the physics needs. It is not a fudge factor and it is not adjustable.
The relation is general to any vibrating string, so yes, provided you supply the unit weight for that specific string and the correct vibrating length. Nylon and gut strings behave differently in terms of stiffness and stretch, but the static tension relation itself is the same.
Yes. When you set the pitch by note name, the frequency comes from twelve-tone equal temperament against the A4 reference you enter. If you tune to a historical or just-intonation scheme, work out the frequency separately and use the hertz input instead.
Not one this page can give you. What a particular neck, top or bridge tolerates depends on its construction, truss rod range, bracing and history. The calculator tells you what a set will pull; whether a given instrument should carry it is a question for a luthier.
This page evaluates a published formula on the numbers you supply and makes no recommendation about strings, gauges, tunings or instrument setup. Unit weight must come from your string manufacturer. Whether any instrument can safely carry a given total tension is a matter for a qualified luthier or repairer, not for a calculator.
