Strain Gauge Calculator

What a bonded strain gauge actually gives you: the resistance change for a strain, the Wheatstone bridge output in mV/V and in millivolts, for quarter, half and full bridges with the real multipliers rather than the rounded ones, the bridge nonlinearity the tables leave out, the amplifier gain to fill an ADC, and what the lead wires and the temperature are doing to all of it.

Last updated 24 Sep 2026

strain gauge bridge

GF, ε, bridge type → mV/V

Bridge arrangement

Gauge factorAbout 2.0 to 2.1 for a constantan foil gauge — the number your gauge’s packet gives, with its own tolerance. Semiconductor gauges reach 100 and more, and are far more temperature-sensitive. Use the figures from your part’s datasheet; typical values vary widely between manufacturers.

Nominal gauge resistance (Ω)120 Ω and 350 Ω are the common foil values; 1,000 Ω gauges cut the excitation current and the self-heating.

Applied strain (µε)One µε is one part per million of length. Structural steel yields at roughly 1,500 µε and aluminium at about 3,500 µε, so a few hundred is a normal working number.

Poisson’s ratio of the test piece0.30 for steel, 0.33 for aluminium, 0.35 for copper, 0.22 for concrete. Only used by the two Poisson arrangements, where the transverse gauge reads −ν times the axial strain.

Bridge excitation voltage (V)5 V and 10 V are usual. More excitation gives proportionally more output and proportionally more self-heating, which is the real limit.

Amplifier output range you want to fill (V)The ADC’s full-scale input, or the range you want the amplifier to swing over at the strain above.

ADC resolution

Lead wiring to the gaugeOnly the quarter bridge cares: its gauge sits at the end of the cable and the cable is inside the bridge arm. A half or full bridge puts all four arms at the gauge, so the leads only carry excitation and output.

Resistance of one lead wire (Ω)Round trip is two of these. 24 AWG copper is about 0.084 Ω per metre, so 10 m of it is 0.84 Ω per lead — already 0.24% of a 350 Ω gauge.

The Wheatstone bridge, with the arms that carry a live gauge marked amber for the arrangement you chose. Excitation across the top and bottom rails, output across the middle. The upper-left arm joins in from the half bridge upwards and the right-hand pair only in the full bridges, which is exactly why the output multiplier goes 1, 1+ν, 2, 2(1+ν), 4. No moving dots are drawn: the interesting current here is the microamp-scale imbalance, not the milliamps flowing down each leg.

0.5244mV/VExample

a quarter bridge, gauge factor 2.10, 350 Ω, 1,000 µε, 5 V excitation, three-wire leads of 0.5 Ω each

The bridge, and the five ways to fill it

x = GF · ε     ΔR = R₀ · x     V_o/V_ex = R₂/(R₁+R₂) − R₄/(R₃+R₄)
quarter: x / (2(2+x))    half Poisson: x(1+ν) / (2(2+x(1−ν)))
half bending: x / 2    full Poisson: x(1+ν) / (2+x(1−ν))    full bending: x
small-strain multipliers against the quarter bridge: 1, 1+ν, 2, 2(1+ν), 4

GF: gauge factor, (ΔR/R)/ε. About 2.1 for constantan foil, so a 1,000 µε strain moves a 350 Ω gauge by about 0.7 Ω
nu: Poisson’s ratio of the specimen. A bar pulled along its axis gets thinner across it by −ν times as much, which is what the transverse gauge in a Poisson bridge reads
x: the fractional resistance change. Every nonlinearity on this page is the x sitting in the denominator, and it is about x/2 as a fraction

Worked example

a quarter bridge, gauge factor 2.10, 350 Ω, 1,000 µε, 5 V excitation, three-wire leads of 0.5 Ω each
x = GF × ε = 2.10 × 1,000 × 10⁻⁶ = 0.002100, so the gauge moves by ΔR = 350 × 0.002100 = 735 mΩ — 0.2100% of its value
A quarter bridge gives V_o/V_ex = x ÷ (2(2+x)) = 0.5244 mV/V. The x in the denominator is the bridge's own nonlinearity: the straight-line answer x/4 would be 0.5250 mV/V, which is 0.105% high
At 5 V excitation that is 2.6222 mV at the bridge terminals — a signal you cannot put anywhere near an ADC without amplifying it
To fill 3.3 V you need a gain of 1,258. One count of a 24-bit converter is then 196.7 nV at the amplifier, 156.3 pV at the bridge, and 0.00006 µε of strain
The leads add 0.5 Ω inside the active arm, which costs 0.143% of the output — 0.5237 mV/V instead of 0.5244. Small, but it is a gain error, not noise, so it does not average away
Each gauge is dissipating 17.86 mW with 14.29 mA through the bridge. That is the figure to watch on a plastic or a composite, where the heat has nowhere to go

The five arrangements, and what each one rejects

“Rejects bending” means an unwanted bending strain cancels; the two bending arrangements are built to measure it, and what they reject is axial load. Every row was computed by solving the bridge as two potential dividers, not from a table, and the Poisson multipliers really are 1+ν and 2(1+ν) rather than the 1, 2 and 4 usually quoted.
Arrangement	Multiplier	Linear?	Rejects temperature?	Rejects bending?	Output at 1,000 µε, GF 2.1
Quarter — 1 active	1	No	No	No	0.5244 mV/V
Half — Poisson pair	1 + ν = 1.30	No	Yes	No	0.6820 mV/V
Half — bending pair	2	Yes	Yes	No — it measures bending	1.0500 mV/V
Full — 2 axial + 2 Poisson	2(1 + ν) = 2.60	No	Yes	No	1.3640 mV/V
Full — 4 active bending	4	Yes	Yes	No — it measures bending	2.1000 mV/V

How small the signal is

One microstrain moves a 350 Ω gauge by about 0.73 milliohms and produces 0.525 µV per volt of excitation out of a quarter bridge — under 3 µV even at a 5 V excitation. That is the whole reason strain instrumentation looks the way it does.
Strain	ΔR on a 350 Ω gauge	Quarter bridge	Full bending bridge	At 5 V excitation (quarter)
1 µε	735 µΩ	0.0005 mV/V	0.0021 mV/V	2.625 µV
10 µε	7.35 mΩ	0.0052 mV/V	0.0210 mV/V	26.25 µV
100 µε	73.5 mΩ	0.0525 mV/V	0.2100 mV/V	262.5 µV
1000 µε	735 mΩ	0.5244 mV/V	2.1000 mV/V	2.622 mV
3000 µε	2.205 Ω	1.5701 mV/V	6.3000 mV/V	7.85 mV

Why the bridge, and why the arrangement matters more than the gauge

A bonded foil strain gauge is a thin serpentine of constantan glued to whatever you want to measure. Stretch the metal and the foil stretches with it; the track gets longer and thinner and its resistance rises. The gauge factor is the constant of proportionality, (ΔR/R)/ε, and for constantan it is about 2.1 — almost all of which is the geometry change, with only a small piezoresistive contribution. That is the whole physics. Everything else is the consequence of the number being tiny: a strain of 1,000 µε, which is a serious working load in steel, changes a 350 Ω gauge by about 0.7 Ω.

Why a bridge and not an ohmmeter. You cannot measure 0.7 Ω on top of 350 Ω to any useful precision, but you can null the 350 Ω out and measure what is left. That is what a Wheatstone bridge does: two potential dividers from the same supply, and you read the difference between their midpoints. The output is proportional to excitation, which is why it is quoted in millivolts per volt — a ratio, independent of the supply, which also means a supply that drifts does not matter if you measure ratiometrically. The same trick makes a platinum RTD readable, for exactly the same reason.

The multiplier is the design decision. One active gauge gives x/4. Two active gauges in adjacent arms, strained in opposite directions, give x/2 — and, because the two arms move oppositely, the x cancels out of the denominator and the output becomes exactly linear. Four active gauges give x: four times the quarter bridge, still exactly linear. In between sit the Poisson arrangements, where the second gauge is turned across the specimen and reads −ν times the axial strain; those give 1+ν and 2(1+ν), about 1.3 and 2.6 in steel. The usual shorthand of “1, 2 or 4” is right for the pure axial and bending cases and wrong for the Poisson ones, which is why all five are on this page.

What each arrangement throws away, which is the real point. A bridge responds to arms moving differently, so anything that moves several arms the same way cancels. Put the two gauges of a half bridge on opposite faces of a beam and wire them into adjacent arms: bending puts one in tension and the other in compression, so the signals add, while a temperature change or an axial pull moves both the same way and cancels. The cancellation is not equally perfect for the two: a uniform resistance drift disappears exactly, while a superimposed axial strain leaves a gain error equal to that strain — 0.17% for an 800 µε pull, against the several hundred per cent error you would have without the cancellation. Put the second gauge across the specimen instead and you cancel temperature but not bending. A quarter bridge cancels nothing at all — a resistance drift of 0.4% on one arm, which is 1.4 Ω out of 350, reads as about 1,900 µε of strain that is not there, far more than most things you are trying to measure. That is why quarter bridges need a gauge whose thermal expansion is matched to the substrate, and why serious work uses half or full bridges.

Lead wires. In a quarter bridge the gauge is at the end of a cable and the cable is inside the bridge arm, so lead resistance both unbalances the bridge and dilutes the gauge factor by R/(R+R_lead). Three-wire connection puts one lead in the active arm and one in the adjacent arm, so the cable’s own temperature coefficient cancels — which matters far more than the residual gain error. Copper’s resistance rises about 0.393% per °C, so two metres of 24 AWG cable there and back — 0.337 Ω — moves by 1.32 mΩ per degree, which a 350 Ω quarter bridge with a gauge factor of 2.1 reads as 1.80 µε per °C of strain that is not there — 36 µε over a 20 °C day. Half and full bridges put all four arms at the gauge, so their leads only carry excitation and output and the problem disappears; on a long cable, sense wires back to the bridge terminals fix the excitation drop too.

Getting it into a converter. Millivolts per volt at single-digit excitation means single-digit millivolts, so an instrumentation amplifier or a bridge-input delta-sigma converter is the back end. The gain figure above fills your range at the strain you entered; what one count is worth then follows from the bit count — and it is worth checking that against physics before buying more bits, because the bridge’s four resistors make Johnson noise of √(4kTR) all by themselves. A 350 Ω bridge at 5 V excitation in a quarter arrangement has a floor of about 0.9 nanostrain per root hertz, while one count of a 24-bit converter spanning 1,000 µε is 60 picostrain. The converter is counting thermal noise fifteen times over. The ADC resolution page has what the bits are really worth once noise is in. For the applied-force version of this same bridge — rated capacity, mV/V and weight rather than gauge factor and strain — see the load cell calculator.

Frequently asked questions

What is the output of a strain gauge bridge in mV/V?

For a quarter bridge it is GF·ε/4 in volts per volt, so about 0.52 mV/V at 1,000 µε with a gauge factor of 2.1. Multiply by 2 for a bending half bridge and by 4 for a full bending bridge. Multiply by the excitation voltage to get millivolts.

What is the gauge factor of a strain gauge?

The ratio of fractional resistance change to strain, (ΔR/R)/ε. Constantan foil gauges are 2.0 to 2.1, karma alloys similar, and silicon semiconductor gauges are 50 to 200 but drift badly with temperature. The value and its tolerance are printed on the gauge packet, and ASTM E251 is the standard that says how it is to be measured.

Quarter, half or full bridge — which should I use?

Full if you can. Four active gauges give four times the output of one, are exactly linear, and cancel temperature and unwanted axial load together. A bending half bridge gives half of that with half the gauges and the same cancellation. A quarter bridge is for when you can only get at one spot, and it needs a temperature-compensated gauge and three-wire connection to be trustworthy.

Why is my quarter bridge nonlinear?

Because the active arm’s own resistance change is in the denominator: the exact output is x/(2(2+x)), not x/4. The error is about x/2, so roughly 0.1% at 1,000 µε and 0.5% at 5,000 µε with a gauge factor of 2.1. It is a known curvature rather than an uncertainty, so it can be corrected — or avoided entirely by using a bending half or full bridge, which are algebraically linear.

How much excitation voltage should I use?

As much as the gauge can dissipate. Power per gauge is V²/4R, so 5 V on a 350 Ω bridge is about 18 mW per gauge — fine on steel, marginal on plastic, too much on a thin composite. Self-heating shows up as slow drift after switch-on. Higher-resistance gauges or pulsed excitation are the way out.

Do the lead wires affect a strain gauge reading?

In a quarter bridge, yes: the leads are inside the bridge arm, so they unbalance the bridge and cut the output by R/(R + R_lead). Worse, copper gains about 0.393% of its resistance per °C, so a two-wire cable turns ambient temperature straight into apparent strain — about 5.3 µε per °C for every ohm of lead in a 350 Ω bridge with a gauge factor of 2.1. Three-wire connection cancels that drift by putting an equal length of the same cable in the adjacent arm; half and full bridges avoid the problem altogether.

Related calculators

References

Micro-Measurements (Vishay Precision Group) Tech Note TN-507-1, Errors Due to Wheatstone Bridge Nonlinearity. Gives the quarter-bridge output as E₀/E = F·ε/(4 + 2F·ε) — identical to the x/(2(2+x)) used here — and states that of its seven gauge arrangements, cases 1, 2, 4 and 5 are intrinsically nonlinear while cases 3, 6 and 7 are linear, which is the same split this page derives.
ASTM E251-20a, Standard Test Methods for Performance Characteristics of Metallic Bonded Resistance Strain Gages. Defines how gauge factor, resistance at reference temperature, the temperature coefficient of gauge factor, transverse sensitivity and thermal output are to be measured — thermal output being, in the standard’s own words, an additive rather than a multiplicative error, which is exactly why a quarter bridge is so exposed to it.
Micro-Measurements Tech Note TN-509, Errors Due to Transverse Sensitivity in Strain Gages — the correction for a gauge’s response to strain across its axis, typically under 10% of the gauge factor but large enough to matter in a biaxial field. Not applied on this page, which assumes a uniaxial strain along the gauge.
Hoffmann K. An Introduction to Measurements using Strain Gages, HBM, 1989 — the standard practical text on bridge arrangements, wiring and compensation, including the three-wire quarter bridge and the reasons for it.