Strain Gauge Calculator

Excitation Voltage (V)

Output Voltage (mV)

Gauge Factor (GF)

Modulus of Elasticity (GPa)

Results will be displayed here.

function calculateStrain() { var vIn = parseFloat(document.getElementById('excitationVoltage').value); var vOut_mV = parseFloat(document.getElementById('outputVoltage').value); var gf = parseFloat(document.getElementById('gaugeFactor').value); var modulusE_GPa = parseFloat(document.getElementById('modulusOfElasticity').value); var resultDiv = document.getElementById('result'); if (isNaN(vIn) || isNaN(vOut_mV) || isNaN(gf) || isNaN(modulusE_GPa)) { resultDiv.innerHTML = 'Please enter valid numbers in all fields.'; return; } if (vIn <= 0 || gf <= 0 || modulusE_GPa <= 0) { resultDiv.innerHTML = 'Excitation Voltage, Gauge Factor, and Modulus of Elasticity must be positive values.'; return; } // Convert units for calculation var vOut_V = vOut_mV / 1000; // Convert millivolts to volts var modulusE_Pa = modulusE_GPa * 1e9; // Convert GigaPascals to Pascals // Calculate Strain (ε) based on a quarter-bridge Wheatstone circuit // Formula: ε = (4 * Vout) / (Vin * GF) var strain = (4 * vOut_V) / (vIn * gf); var microstrain = strain * 1e6; // Convert strain to microstrain (με) // Calculate Stress (σ) using Hooke's Law // Formula: σ = E * ε var stress_Pa = modulusE_Pa * strain; var stress_MPa = stress_Pa / 1e6; // Convert Pascals to MegaPascals (MPa) var resultHTML = '

Calculation Results

' + 'Calculated Strain: ' + microstrain.toFixed(2) + ' με (microstrain)' + 'Calculated Stress: ' + stress_MPa.toFixed(2) + ' MPa (Megapascals)'; resultDiv.innerHTML = resultHTML; }

Understanding Strain and Stress with Strain Gauges

A strain gauge is a sensor used to measure the strain, or deformation, of an object. It operates on the principle of piezoresistivity, where the electrical resistance of a material changes when it is stretched or compressed. By bonding a strain gauge to a material and measuring the change in its resistance, we can accurately determine the amount of strain the material is experiencing. This data is crucial for calculating stress, which is the internal force that particles of a body exert on each other.

The Principle Behind the Calculation

Strain gauges are typically used in a Wheatstone bridge configuration to detect the minute changes in resistance. For a single active gauge (a quarter-bridge setup), the relationship between the bridge's input voltage (excitation), output voltage, and the strain is defined by the gauge factor (GF). The formula used by this calculator is:

Strain (ε) = (4 * V_out) / (V_in * GF)

Here, V_in is the excitation voltage supplied to the bridge, and V_out is the resulting differential voltage, which is directly proportional to the change in resistance and thus the strain.

How to Use the Strain Gauge Calculator

Excitation Voltage (V): Enter the voltage supplied to your Wheatstone bridge circuit. Common values are 5V or 10V.
Output Voltage (mV): Input the measured voltage difference from the bridge output, typically in millivolts (mV).
Gauge Factor (GF): Provide the gauge factor specific to your strain gauge. This value is supplied by the manufacturer and is usually around 2.0.
Modulus of Elasticity (GPa): Enter the Young's Modulus (or Modulus of Elasticity) of the material to which the gauge is bonded. This is required to calculate stress from strain. For example, steel is approximately 200 GPa, and aluminum is around 70 GPa.

Example Calculation

Let's consider a strain gauge bonded to a steel beam. We apply the following parameters:

Excitation Voltage (V_in): 10 V
Measured Output Voltage (V_out): 5 mV
Gauge Factor (GF): 2.05
Modulus of Elasticity for Steel (E): 200 GPa

First, we calculate the strain:

ε = (4 * 0.005 V) / (10 V * 2.05) = 0.02 / 20.5 ≈ 0.0009756

In microstrain, this is 0.0009756 * 1,000,000 = 975.61 με.

Next, we calculate the stress using Hooke's Law (σ = E * ε):

σ = (200 * 10⁹ Pa) * 0.0009756 ≈ 195,121,951 Pa

In Megapascals, this is 195,121,951 / 1,000,000 = 195.12 MPa.

Common Applications of Strain Gauges

Strain gauges are fundamental components in many measurement and testing applications across various industries, including:

Structural Health Monitoring: Assessing the integrity and safety of bridges, buildings, and aircraft wings.
Load Cells and Scales: Used in weighing systems, from kitchen scales to industrial truck scales.
Torque and Power Measurement: Measuring the torque on rotating shafts in engines and machinery.
Pressure Transducers: Measuring fluid or gas pressure by detecting the deformation of a diaphragm.
Biomedical Engineering: Analyzing forces on bones, implants, and medical devices.