Guitar & Bass String Tension and Gauge Calculator

For each active string, use Mersenne’s law in the archived D’Addario chart convention:

Here $L$ is the nut-to-saddle vibrating length in inches, $f$ is hertz, $UW$ is the chart’s lb/in, and $T$ is lbf. The step $k_{us}$ carries the mass-to-force conversion units lb·in/(lbf·s²), so the calculation remains dimensionally explicit. D’Addario’s rounded coefficient 386.4 is retained exactly for chart comparisons; it differs by about 0.08% from a calculation using exact standard-gravity conversions. Force display uses the unit library’s lbf-to-N conversion, rather than the brochure’s rounded 4.45 factor.

Note frequencies are $f=A4\,2^{(m-69)/12}$, where $m$ is the MIDI note number (UNSW Music Acoustics). Individual frequency entry bypasses this note conversion. Each string may have its own scale length.

In gauge-design mode, search only the chosen PL, NW or XLB family and minimize $|UW-UW_{\rm req}|$. At fixed pitch and scale this also minimizes absolute tension error. Use the selected row’s actual weight to calculate achieved tension; do not scale a wound-string diameter to invent a gauge. Exact ties keep the first chart row. Out-of-range requests return the nearest endpoint with a warning.

Set spread is $T_{\max}-T_{\min}$; relative spread is 100 times that value divided by mean tension. Target error is $100(T/T_{\rm target}-1)$. The neck colours use $T/T_{\rm target}$, clamped to a 0.5–1.5 display scale. Geometry is schematic; string lengths are proportional, while spacing and line thickness are enlarged for readability.

Manufacturer method and unit weights: attached source s5 pp. 118–120 and 124 (D’Addario printed pp. 4–6 and 10).

• A uniform, flexible string vibrates at small amplitude between fixed endpoints, with static tension and a known fundamental frequency.
• Unit weight refers to the actual speaking portion of the string. A taper or exposed core within that portion requires more information than one uniform weight.
• The built-in 80 rows are archived D’Addario PL plain-steel, NW nickel-wound guitar and XLB nickel-wound bass data. They are not guaranteed specifications for current production or another brand. Gauge is decoded from the manufacturer part number.
• A custom forward-mode string uses the entered unit weight directly. Its diameter is reported and controls schematic line thickness only; it does not determine mass.
• Equal target tension is a user-selected design objective, not a universal definition of a balanced playing feel.

Use for comparing open-string static tensions and selecting candidates from the published families. Input ranges of 5–50 in scale, 10–2000 Hz frequency and 0.1–100 lbf target are numerical entry limits, not ratings of strings or instruments.

The model excludes bending stiffness and inharmonicity, fretting stretch, pluck-induced tension changes, friction, break-angle forces, thermal effects, material strength, fatigue and neck/bridge deformation. A total axial load does not establish structural safety. Confirm product availability, winding length, taper location, nut-slot fit and the instrument maker’s limits independently.

The reference cases use independently published rounded chart tensions, not expectations generated from this calculator. Small differences follow from rounded chart notes and tensions. There is no animation because this is static set sizing.