Guitar & Bass String Gauge Tension Calculator: Scale Length, Pitch & Pounds-Per-String Setup Guide (2026)

Choosing between a .009–.042 Super Light set, a .010–.046 Regular Light set, or a .011–.052 Medium set is not guesswork—it is pure mechanical physics. Every guitar and bass neck is a balanced lever system where total forward string pull (typically 85 lbs to 165 lbs on 6-string guitars and 160 lbs to 215 lbs on electric basses) is counteracted by an internal steel truss rod and tremolo claw springs. Use the interactive Mersenne's Law string tension calculator below alongside our Online Guitar Tuner, Online Bass Tuner, and Alternate Tuning Frequency Chart to calculate exact per-string pounds (`lbs`) and kilograms (`kg`) across any scale length and tuning preset.

Mersenne's Law Explained: How Unit Weight, Scale Length & Pitch Determine String Tension

Published by French polymath Marin Mersenne in Harmonie universelle (1636), the acoustic equation for a stretched vibrating string relates fundamental frequency ($f$, in Hertz), speaking length between the nut and bridge saddle ($L$, in inches), linear unit weight ($UW$, in pounds per linear inch), and gravitational acceleration ($g = 386.088\text{ in/s}^2$) to mechanical tension ($T$, in pounds-force):

Every variable in this equation gives luthiers and players a direct mechanical lever over fretboard playability and acoustic tone:

• Unit Weight ($UW$) and Core-to-Wrap Ratios: For plain steel treble strings (`E4, B3, G3`), unit weight scales directly with the cross-sectional area of high-carbon steel ($\pi r^2 \times \rho_{\text{steel}}$), meaning a `.010"` string has $(0.010 / 0.009)^2 = 1.2346$, or 23.5% more mass and tension than a `.009"` string at the same pitch! For wound bass strings (`D3, A2, E2`), total mass is the sum of the hexagonal or round steel core wire plus the outer nickel-plated steel or 80/20 bronze wrap wire.
• Scale Length Squared ($L^2$): Moving from a 24.75" Gibson Les Paul scale to a 25.50" Fender Stratocaster scale increases speaking length by only 3.03%, yet increases tension at the exact same pitch and gauge by $(25.50 / 24.75)^2 - 1 = \mathbf{+6.15\%}$. Moving from `25.50"` to a `27.00"` Baritone scale increases tension at the same pitch by $(27.00 / 25.50)^2 - 1 = \mathbf{+12.11\%}$, which is why baritones can tune down a fourth to `B1 Standard (B1-E2-A2-D3-F#3-B3)` without requiring unplayably thick bridge-cable strings.
• Frequency Squared ($f^2$): Each semitone step upward increases string tension by $2^{2/12} - 1 = \mathbf{+12.25\%}$, while each semitone step downward reduces string tension by $1 - 2^{-2/12} = \mathbf{-10.91\%}$.

Standard String Gauge Pack Tension Comparison Chart (E440 Standard Tuning)

Compare per-string and total neck load across the five most popular electric, acoustic, and 4-string bass gauge packs below, and verify your open-string calibration on our Online Guitar Tuner or Online Bass Tuner:

Why Plain G3 Strings Feel Stiff and How Balanced Tension Sets Solve It

Look closely at the per-string tension figures for a traditional .010–.046 electric guitar pack at 25.5" scale length: the 2nd string (`B3, .013"`) sits at 15.4 lbs, the 4th string (`D3, .026w"`) sits at 18.4 lbs, and the 5th string (`A2, .036w"`) spikes to 19.5 lbs, before the 6th string (`E2, .046w"`) drops back down to 17.5 lbs. Historically, string manufacturers assembled packs using even thousandth-of-an-inch gauge increments rather than equalized mechanical tension.

Even more noticeable is the unwound .017" or .018" G3 string. Because an unwound solid steel cylinder of `.017"` diameter has much higher flexural bending rigidity (inharmonicity) than a thin `.009"` core wrapped in flexible nickel wire, a plain G3 string resists finger vibrato and exhibits a pronounced +20 cent sharp pitch chirp when picked hard. Switching to a balanced tension set (such as `.010 - .0135 - .017 - .025w - .034w - .046w`) or using a wound .020w" or .022w" G3 string for jazz and D-Standard setups equalizes right-hand pick bounce and improves chord intonation across the 2nd through 7th frets.

Nut Slot Width, Tremolo Claw Springs & Intonation Adjustments After Changing Gauges

1. Check Nut Slot Binding on Wound Strings: Jumping from a .009–.042 pack to a .011–.052 or .012–.056 pack increases string diameter by `.010"` to `.014"` on the low E and A strings. If a thicker wound string pinches inside a narrow bone or synthetic nut slot, it will bind when you turn the tuning peg and ping out of tune after a string bend. Apply dry graphite (pencil lead) or PTFE nut lubricant, or have a luthier widen the nut slots with gauged nut files to `.002"` wider than the string diameter.
2. Re-Level Floating Tremolo Bridges: Increasing total neck load from 85.1 lbs (.009s) to 103.6 lbs (.010s) adds +18.5 lbs of forward pull on a Stratocaster or Floyd Rose bridge, lifting the rear of the bridge plate off the body. Remove the rear spring cavity cover and tighten the two tremolo claw wood screws clockwise by 1.5 to 2.5 turns (or add a fourth tremolo spring) until the bridge plate sits parallel to the guitar top at concert pitch.
3. Fine-Tune Bridge Saddle Compensation: Higher-mass strings have greater flexural stiffness at the termination points, requiring slightly longer speaking length to intonate accurately at the 12th fret. Use our Online Guitar Tuner in sustain-lock mode to compare the 12th-fret harmonic against the fretted 12th-fret note and move the saddle backward slightly if the fretted note reads sharp.