Guitar & Musical String Tension (T = μ × (2Lf)² / 386.4 lbs) Scale Length Calculator

Compute guitar/bass string tension (lbs & kg) from scale length, pitch frequency Hz, and gauge weight.

String Tension at Pitch
16.3 lbs
String Tension in Kilograms-Force 7.4 kgf
String Tension in Newtons 72.53 N
Tension if Down-Tuned 1 Half-Step (−1 Semitone) 14.53 lbs
Inputs
⚡ Scenarios:
in
Instrument vibrating scale length in inches (25.5" Fender, 24.75" Gibson, 34" Bass).
Hz
Target open-string fundamental frequency in Hz (E4=329.63, B3=246.94, G3=196.00, D3=146.83, A2=110.00, E2=82.41).
in gauge
Plain steel string diameter gauge in inches (e.g., 0.010 for a .010 high E string).
Results & Graph
String Tension at Pitch
16.3 lbs
String Tension in Kilograms-Force
7.4 kgf
String Tension in Newtons
72.53 N
Tension if Down-Tuned 1 Half-Step (−1 Semitone)
14.53 lbs

String Tension at Pitch

Graph 1 • Guitar String Tension & Scale • Domain Architecture & Live Telemetry Maps Scale Length Inches, Target Pitch Frequency Hz, String Diameter Gauge Inches through Guitar String Tension & Scale Formula.
PETS, VEHICLES & LIFESTYLE String Tension at Pitch 16.3 lbs String Tension in Kilogram 7.4 kgf Guitar String Tension & Scale • Component Waterfall String Tension at Pitch 16.3 lbs String Tension in Kilograms-Fo 7.4 kgf String Tension in Newtons 72.53 N Tension if Down-Tuned 1 Half-S 14.53 lbs
Graph 2 • String Tension at Pitch Across Scale Length Inches Sweep (40% → 160%) Evaluates Tension_lbs = [ UnitWeight_lb_per_in × (2 × ScaleLength_in × Frequency_H across 7 operating points (current input highlighted).
0 lbs 22.96 lbs 45.91 lbs 3.61 10.20in 5.87 15.30in 10.43 20.40in 16.30 25.50in 23.48 30.60in 31.96 35.70in 41.74 40.80in
Graph 3 • Joint Sensitivity: Scale Length Inches × Target Pitch Frequency Hz Compares String Tension at Pitch when Target Pitch Frequency Hz is shifted +25% (solid) vs. −25% (dashed).
0 lbs 23.68 lbs 47.36 lbs --- Target Pitch Frequency Hz @ 75% 12.48 -30% 18.41 -15% 25.47 +0% 33.67 +15% 43.05 +30%
Summary: A 0.01" steel string on a 25.5" scale tuned to 329.63 Hz exerts 16.3 lbs (7.4 kg / 72.5 N) of neck tension.
Summary: A 0.01" steel string on a 25.5" scale tuned to 329.63 Hz exerts 16.3 lbs (7.4 kg / 72.5 N) of neck tension.
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Interactive chart & math engine powered by CalculatorGraph

Formula & Mathematical Methodology: Guitar String Tension & Scale Formula

Tensionlbs = [ UnitWeightlbperin × (2 × ScaleLengthin × FrequencyHz)² ] / 386.088
Tension_lbs = [ UnitWeight_lb_per_in × (2 × ScaleLength_in × Frequency_Hz)² ] / 386.088
  • scaleLengthInches: Instrument vibrating scale length in inches (25.5" Fender, 24.75" Gibson, 34" Bass).
  • targetPitchFrequencyHz: Target open-string fundamental frequency in Hz (E4=329.63, B3=246.94, G3=196.00, D3=146.83, A2=110.00, E2=82.41).
  • stringDiameterGaugeInches: Plain steel string diameter gauge in inches (e.g., 0.010 for a .010 high E string).

Rounding: Internal floating-point calculations preserve full precision; currency and percentage outputs round to 2 decimal places.

Worked Example: Guitar String Tension & Scale Worked Example

Compute guitar/bass string tension (lbs & kg) from scale length, pitch frequency Hz, and gauge weight.

  1. Enter your operational, financial, or physical measurement inputs.
  2. Apply the standard domain equation: Tension_lbs = [ UnitWeight_lb_per_in × (2 × ScaleLength_in × Frequency_Hz)² ] / 386.088.
  3. Review the primary result, sensitivity metrics, and 3 interactive SVG graphs.
Result: Calculates Guitar String Tension & Scale via Tension_lbs = [ UnitWeight_lb_per_in × (2 × ScaleLength_in × Frequency_Hz)² ] / 386.088.

Frequently Asked Questions

How does the Guitar & Musical String Tension (T = μ × (2Lf)² / 386.4 lbs) Scale Length Calculator calculate results?

It computes Tension_lbs = [ UnitWeight_lb_per_in × (2 × ScaleLength_in × Frequency_Hz)² ] / 386.088 directly in your browser and updates three custom SVG visualizations in real time.

Can I use Goal Seek to solve backwards for any input variable?

Yes. Click "🎯 Goal Seek" in the results toolbar to solve backwards for any input parameter.

Are my business and personal numbers kept private?

Yes. All calculations execute 100% locally in your browser with zero server transmission.

Everyday Life · Pets, Vehicles & Lifestyle

Guitar & Musical String Tension (T = μ × (2Lf)² / 386.4 lbs) Scale Length Calculator: inputs, method, and how to read the result

Compute guitar/bass string tension (lbs & kg) from scale length, pitch frequency Hz, and gauge weight.

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Scale Length Inches: Instrument vibrating scale length in inches (25.5" Fender, 24.75" Gibson, 34" Bass).
  • Target Pitch Frequency Hz: Target open-string fundamental frequency in Hz (E4=329.63, B3=246.94, G3=196.00, D3=146.83, A2=110.00, E2=82.41).
  • String Diameter Gauge Inches: Plain steel string diameter gauge in inches (e.g., 0.010 for a .010 high E string).

What the calculation includes

With the default values shown, String Tension at Pitch is 16.3 lbs. The calculation follows Guitar String Tension & Scale Formula; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Scale Length Inches from 25.5 in to 28.05 in changes String Tension at Pitch from 16.3 lbs to 19.73 lbs. This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses industry-standard APICS/ASCM supply chain, lean manufacturing, and consumer physics formulas.
  • Actual commercial freight tariffs, marketplace commissions, and utility rates vary by carrier and contract.

Scope: Global Supply Chain, Business & Consumer Standard Check the assumptions and limitations against your situation before relying on the estimate.

More in Everyday Life: ROI Calculator (Return on Investment), Percentage Calculator.