Guitar String Tension: Formula, Data and Practical Comparisons
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String tension is the pulling force a string puts on the guitar when it is tuned to pitch. It shapes how stiff a string feels, how much effort bends take, and how evenly a set feels across the neck. You can calculate it from three numbers.
The Tension Formula
T = UW × (2 × L × f)² / 386.4
| Symbol | Meaning | Unit |
|---|---|---|
| T | Tension | pounds-force (lbf) |
| UW | Unit weight, the string’s mass per length | lb/in |
| L | Scale length | inches |
| f | Frequency of the note | Hz |
The constant 386.4 converts the result into pounds-force. To get newtons, multiply by 4.44822.
Why Gauge Alone Is Not Enough
Gauge is just the diameter. A wound string’s mass depends on its core wire, its wrap wire, and how they are built, so two wound strings with the same gauge can weigh different amounts. That is why the formula needs unit weight rather than gauge. Use the unit weight the manufacturer publishes for the exact string you are checking.
Worked Example: Plain .010 High E
The unit weights below come from a historical D’Addario catalog chart, mirrored here. These are archived figures, and current products may differ.
PL010, UW 0.00002215 lb/in, 25.5 inch scale, tuned to E4 (329.63 Hz):
- 2 × 25.5 × 329.63 = 16,810.1
- 16,810.1² ≈ 282,580,000
- 282,580,000 × 0.00002215 ≈ 6,259
- 6,259 / 386.4 ≈ 16.2 lbf (about 72.1 N)
Worked Example: Wound .046 Low E
NW046, archived UW 0.00038216 lb/in, 25.5 inch scale, tuned to E2 (82.41 Hz):
- 2 × 25.5 × 82.41 = 4,202.9
- 4,202.9² ≈ 17,664,000
- 17,664,000 × 0.00038216 ≈ 6,751
- 6,751 / 386.4 ≈ 17.5 lbf (about 77.7 N)
The .046 is more than four times thicker than the .010, yet the two tensions are close. Pitch and unit weight balance each other out, and that balance is what manufacturers aim for when they design a set.
Practical Comparisons
Because scale length and frequency are both squared, small changes in either have a noticeable effect. The figures below are calculated from the formula and the archived PL010 unit weight:
| Setup | Multiplier | .010 high E tension |
|---|---|---|
| 25.5 in, standard tuning | 1.000 | 16.2 lbf |
| 24.75 in, standard tuning | 0.942 | 15.3 lbf |
| 25.5 in, down a half step | 0.891 | 14.4 lbf |
| 25.5 in, down a whole step | 0.794 | 12.9 lbf |
| 24.75 in, down a half step | 0.839 | 13.6 lbf |
The multiplier for scale length is (new length / old length)². For tuning, each half step down multiplies tension by about 0.891. So if you tune down and want the same feel, you will usually need a heavier gauge. A shorter scale gives a similar loosening effect at the same pitch. Our guitar scale length guide explains how common scales compare, and the guitar string gauge chart lists typical set gauges.
Drop C is a common case where this math matters. Every string sits at least a whole step below standard and the low string drops two whole steps, so tension falls well below that of a standard set. The string gauge for Drop C guide uses the same scale length ratio to suggest heavier starting sets for that tuning.
Calculating Your Own Set
The string tension calculator runs this formula for you, so you can compare strings, scales, and tunings without doing the math by hand. The tool uses the archived PL and NW weights above, not user-entered current manufacturer weights. For an exact current product, use its maker’s published tension data or apply the formula to its current unit weights.