Load Cell Calculator
Load Cell Calculator
What a load cell gives you and what a converter can do with it: the output voltage at any load from the rated capacity, the rated output in mV/V and the excitation, the amplifier gain that fills an ADC’s range, the smallest weight one count represents, and the far smaller number of divisions the noise actually leaves you with.
load cell output
4 × 200 kg cells at 2.0 mV/V on 5 V, 500 kg on the platform, gain 128 into a 24-bit converter with a 2.5 V range and 60 nV of noise
One proportion, and what the converter makes of it
gain = ADC range ÷ FSO LSB = ADC range ÷ 2N
weight per count = Emax × LSB ÷ (gain × FSO)
noise-free divisions = FSO ÷ (6.6 σ) — the gain cancels
n cells in parallel: Emax,system = n·Emax, mV/V unchanged
- FSO
- full-scale output: the bridge voltage at rated capacity. A 2 mV/V cell on 5 V gives 10 mV, which is the whole signal you have to work with
- sigma
- RMS noise of the front end referred to its input. 6.6σ is the peak-to-peak spread you see over a few thousand readings, which is what sets a stable display
- E max
- rated capacity. OIML R 60 calls it E_max and defines the division count n_LC against it
Worked example
4 × 200 kg cells at 2.0 mV/V on 5 V, 500 kg on the platform, gain 128 into a 24-bit converter with a 2.5 V range and 60 nV of noise
Full-scale output is 2.0 mV/V × 5 V = 10 mV — and it stays 10 mV however many cells you parallel, because their outputs average while their capacities add. System capacity is 4 × 200 = 800 kg
500 kg is 62.5% of that, so the bridge gives 10 mV × 0.6250 = 6.25 mV
A gain of 128 makes that 800 mV, and at capacity 1.28 V — 51.2% of the converter's 2.5 V range. Filling it exactly would need a gain of 250
One count of 24 bits is 149 nV, which referred back through the gain is 1.164 nV at the cell — 0.0931 g. Zero to capacity is 8,589,935 counts
But 60 nV RMS of front-end noise allows only FSO ÷ 6.6σ = 25,253 divisions — 340 times fewer than the converter can count — which in weight is 32 g, not 0.0931 g. The gain cancels out of that ratio entirely: turning it up amplifies the noise with the signal
And you are only using 63% of the capacity, so over the range you actually weigh there are about 15,783 divisions. Keep a ten-to-one margin between internal and displayed resolution and the display can carry roughly 1,578 steps
Full-scale output, which is all the signal there is
| Rated output | At 5 V | At 10 V | At 12 V | Gauge strain at capacity (GF 2.1) |
|---|---|---|---|---|
| 1.0 mV/V | 5 mV | 10 mV | 12 mV | 476 µε |
| 1.5 mV/V | 7.5 mV | 15 mV | 18 mV | 714 µε |
| 2.0 mV/V | 10 mV | 20 mV | 24 mV | 952 µε |
| 3.0 mV/V | 15 mV | 30 mV | 36 mV | 1,429 µε |
| 4.0 mV/V | 20 mV | 40 mV | 48 mV | 1,905 µε |
OIML R 60 accuracy classes
| Class | Division count n_LC | Typically |
|---|---|---|
| A | 50,000 and above | Reference and laboratory work |
| B | 5,000 to 100,000 | Precision and laboratory balances |
| C | 500 to 10,000 | Industrial and trade scales — C3 (3,000) is the workhorse |
| D | 100 to 1,000 | Coarse weighing |
From millivolts per volt to something you can display
A load cell is a piece of steel machined so that a known load produces a known strain, with four strain gauges bonded to it in a full bridge. The manufacturer has already done the mechanics and the calibration, so what you are handed is two numbers: a rated capacity and a rated output in millivolts per volt of excitation. Between zero and capacity the output is proportional, so the whole of this page is one proportion and the interesting question is entirely about the electronics hanging off it. For the bridge itself — gauge factor, the multiplier, why the arrangement is a full bending bridge — see the strain gauge calculator; this page is the applied-force end of the same device.
How little signal there is. A 2 mV/V cell on 5 V excitation gives 10 mV at its rated capacity. Not 10 mV per kilogram — 10 mV for the whole range. A 200 kg cell therefore gives 50 µV per kilogram and 50 nV per gram, which is why weighing electronics is a specialist business and why the converter is usually a 24-bit delta-sigma part with a gain stage in front of it.
Excitation cancels if you let it. Output is proportional to excitation, so an excitation that drifts 0.1% shifts every reading 0.1%. The standard fix is ratiometric measurement: derive the ADC’s reference from the same supply that excites the bridge, and the ratio cancels exactly. It is the single most valuable thing you can do to a weighing front end, and it is free.
Counts are not divisions. These get confused constantly. The count figure is arithmetic: the converter’s range divided by its LSB. The division figure is physics: the full-scale output divided by the peak-to-peak noise, conventionally 6.6 times the RMS value. With a 2 mV/V cell at 5 V and 60 nV RMS of front-end noise you get about 25,253 noise-free divisions, and a 24-bit converter at gain 128 counts several hundred times more steps than that. Raising the gain does not help, and the reason is worth seeing algebraically: the noise-free division count is FSO/(6.6σ), and the gain does not appear in it at all. Gain amplifies the noise and the signal together. What does help is a lower noise front end, a slower output rate, more excitation (up to the cell’s self-heating limit) or a cell with a higher mV/V.
Capacity you do not use is resolution you do not get. A cell is sized for the worst case, but the divisions are spread over the whole capacity whether you use it or not. Four 200 kg cells under a platform give 800 kg of capacity; if the platform and frame weigh 150 kg and you only ever weigh 100 kg of product, you are resolving 100 kg with divisions sized for 800. Everything — dead load, the hopper, the frame, the safety margin — comes out of the same budget. Size the cells as close to the real maximum as the overload rating allows.
Several cells. Wire n identical cells in parallel and their outputs average while their capacities add, so the system still reads the same millivolts per volt and the system capacity is n times one cell. That also means the weight per count multiplies by n: four cells of 200 kg resolve four times as coarsely as one 200 kg cell would. The cells have to be matched in sensitivity, or the reading depends on where the load sits on the platform — corner adjustment, usually a small trim resistor in series with one cell’s output, is what fixes that. The excitation current multiplies by n too, which is why a four-cell system on 350 Ω cells draws four times the current a single cell does and why 700 Ω and 1,000 Ω cells exist.
For what the converter’s bits are really worth once noise is in, the ADC resolution calculator covers ENOB, oversampling and noise-free resolution in general; for a sensor sent down a long cable as a current instead of a voltage, the 4–20 mA loop calculator.
Frequently asked questions
What does mV/V mean on a load cell?
Millivolts of bridge output per volt of excitation, at the cell’s rated capacity. A 2 mV/V cell excited at 10 V gives 20 mV when fully loaded, and proportionally less below that. It is a ratio rather than a voltage precisely so that the excitation can be whatever your electronics prefers.
How do I calculate load cell output voltage?
Output = (rated mV/V ÷ 1,000) × excitation × (load ÷ capacity). With several cells in parallel, use the system capacity — the rated output per volt does not change when you parallel matched cells.
What gain do I need for a load cell amplifier?
The converter’s full-scale input range divided by the cell’s full-scale output. A 2 mV/V cell on 5 V gives 10 mV, so a ±2.5 V converter needs a gain of 250. Gains of 128 are common because bridge ADCs offer them; that leaves about half the range unused, which costs a bit but not as much as the noise does.
Why does my 24-bit scale only resolve a few thousand steps?
Because bits count and noise resolves, and they are different things. The usable division count is the full-scale output divided by about 6.6 times the front end’s RMS noise, and the amplifier gain cancels out of it completely. 24 bits at gain 128 might count eight million steps while the noise allows twenty-five thousand — and good weighing practice then displays about a tenth of that again, so the last digit stays still.
How do I connect several load cells?
In parallel, through a summing (junction) box: excitation in parallel, outputs in parallel. The system reads the same mV/V as one cell and has n times the capacity. The cells must be sensitivity-matched, or corner-trimmed with a series resistor on the high ones, otherwise the reading depends on where the load sits.
What is a C3 load cell?
An OIML R 60 class C cell certified for 3,000 verification intervals. Class C spans 500 to 10,000 intervals and covers most industrial and trade weighing; class B and A are for laboratory work. The class is a metrological qualification of the cell over temperature, creep and repeatability, and has nothing to do with how many counts your converter produces.
Related calculators
References
- OIML R 60-1:2021, Metrological regulation for load cells — Part 1: Metrological and technical requirements. Defines maximum capacity E_max, the minimum load cell verification interval v_min, the maximum number of verification intervals n_LC, and Table 1’s accuracy classes: A from 50,000 up, B from 5,000 to 100,000, C from 500 to 10,000 and D from 100 to 1,000.
- Texas Instruments white paper SBAA154 (June 2007), Load Cell Output Voltage / Excitation Voltage. States the mV/V convention, works the example that a 4 mV/V cell excited at 5 V has a full-scale output of only 20 mV and that 20,000 counts of resolution therefore needs the digitiser to resolve 1,000 nV repeatably, and makes the point that a good scale design keeps internal resolution about ten times finer than the displayed value.
- Micro-Measurements (Vishay Precision Group) Tech Note TN-507-1, Errors Due to Wheatstone Bridge Nonlinearity — the bridge behind the rated output, and the reason a load cell’s four-active-gauge bending bridge is algebraically linear where a single gauge is not.
- OIML R 76-1:2006, Non-automatic weighing instruments — Part 1: Metrological and technical requirements and tests: the companion recommendation that governs the whole instrument rather than the cell, and where the number of verification scale intervals a scale may display is set.