Selecting a Precision Balance: 0.1 mg Readability at 60 g

A 60 g load displayed to 0.1 mg with a 2 mg accuracy target calls for a four-place analytical balance whose weighing capacity covers the sample plus any container tare. Mettler Toledo is not the only source. Sartorius, Precisa, Ohaus, Radwag, Precia Molen, Arpège Master K, Bilanciai / Gibertini and Gram also sell precision weighing instruments. The display resolution is the easy part of the specification. The 2 mg limit is decided by repeatability, linearity, temperature drift, eccentric loading and air buoyancy, so compare those datasheet figures across vendors, not the displayed digits.

Readability, Repeatability and Accuracy in a 60 g Specification

Readability (d) is the smallest display increment. Here it is 0.1 mg, so the 60 g reading shows 60.0000 g. Accuracy is how close the indicated value is to the true or conventional mass of the sample. On a balance, accuracy is expressed as a measurement uncertainty built from several separate error terms. A 0.1 mg display does not deliver 0.1 mg accuracy. It gives resolution 20 times finer than the 2 mg tolerance, and that ratio is a sound design margin.

Error Sources in a Four-Place Weighing

A four-place balance uses an electromagnetic force-restoration cell. A coil current holds the pan at a fixed position, and that current is proportional to the downward force. Anything else that adds force or changes the coil-to-force relationship shows up as mass. The three main disturbances are air currents, convection from a sample warmer or colder than the chamber, and electrostatic charge on plastics or powders. Changes in the magnet and coil with temperature shift the sensitivity. Internal motorised adjustment weights correct this drift when adjustment is triggered.

Combine the independent terms as a root-sum-square. Convert each rectangular-limit term to a standard uncertainty by dividing by √3, then apply a coverage factor k = 2:

u_c = sqrt( s_rep^2 + (L/√3)^2 + (E/√3)^2 + (TC·ΔT·m/√3)^2 + u_buoy^2 )
U   = 2 · u_c        → requirement: U ≤ 2 mg

s_rep = repeatability (std. dev.)   L = linearity limit
E     = eccentricity limit          TC = sensitivity drift (ppm/K)
ΔT    = room temperature swing since last adjustment
m     = 60 g

Air buoyancy is the term most often left out. Balances are adjusted to conventional mass. This convention assumes reference weights of density 8000 kg/m³ weighed in air of 1.2 kg/m³. A sample of different density receives a different upthrust. The relative correction is approximately ρ_air·(1/ρ_sample − 1/8000):

First decide what the 2 mg tolerance applies to. If it applies to conventional mass, or to comparisons between samples of the same material, the buoyancy correction cancels and can be ignored. If it applies to true mass of a low-density sample, the correction is many times the tolerance. Air-density variation also matters. Assuming a 0.02 kg/m³ day-to-day change, a water-density sample moves by about 1 mg at 60 g, which is half the budget. For true-mass work, measure air temperature, pressure and humidity and apply the correction.

Vendor Screening Procedure for a 60 g / 2 mg Balance

1. Fix the capacity. Take 60 g, add the heaviest container or fixture tare, and add headroom. Choose the smallest 0.1 mg capacity class that exceeds this total. At constant readability, a larger capacity usually brings poorer repeatability.
2. Ask each vendor for a datasheet or quotation of a 0.1 mg model. Candidates include Sartorius, Precisa, Ohaus, Radwag, Precia Molen, Arpège Master K, Bilanciai / Gibertini and Gram. Some of these brands focus on industrial scales, so confirm that their current range includes a four-place analytical balance at the required capacity.
3. Enter each vendor's repeatability, linearity, eccentricity and ppm/K drift into the budget above. Use a realistic ΔT for the room. Reject any model where U exceeds 2 mg. As a design choice, keep U at or below roughly two thirds of the tolerance so that ageing and site conditions have margin.
4. Prefer internal adjustment with a temperature or time trigger. It holds the TC·ΔT term near zero without operator action.
5. Check for a closed draft shield, a level indicator, an interface for data logging (serial or USB), and an optional ionizer if samples are plastic or powder.
6. Specify a calibrated reference weight near 60 g. Its certificate uncertainty should be small compared with 2 mg. This weight is used for acceptance and routine checks.

Acceptance Checks on the Installed Balance

1. Location: rigid weighing table, away from doors, HVAC outlets and sunlight. Expected result: the zero reading is stable to the last digit or two with the draft shield doors closed.
2. Level: adjust the feet until the level bubble is centred. Expected result: the bubble is inside the ring. Re-run internal adjustment after any levelling.
3. Warm-up: keep the balance powered for the warm-up time stated in the manual before testing. Expected result: zero drift is flat after the doors close.
4. Adjustment: run internal adjustment, or external adjustment with the certified weight. Expected result: the adjustment completes with no error message.
5. Repeatability: make 10 placements of the reference weight near 60 g, re-zeroing between placements. Expected result: the standard deviation is at or below the value used in your uncertainty budget. As an illustration, s_rep ≤ 0.3 mg keeps 2·s_rep inside one third of the tolerance.
6. Eccentricity: place the weight at the centre and then at four positions midway to the pan edge. Expected result: the maximum spread is within the datasheet eccentricity limit and well under 2 mg.
7. Span error: compare the indication for the reference weight with its certificate value. Expected result: the difference is inside the combined linearity specification plus the certificate uncertainty.
8. Tare path: tare the empty container, add the reference weight, and read the net value. Expected result: the net value matches the step 7 indication within repeatability.

Recurring Faults with Four-Place Balances

• Treating readability as accuracy. Buying on displayed digits alone is wrong practice. Two balances with 0.1 mg readability can differ severalfold in repeatability and drift.
• Weighing samples that are not at room temperature. A warm part creates an updraft and reads light, and the reading creeps as the part cools. Let samples reach chamber temperature before weighing.
• Electrostatic charge. Plastic containers and dry powders give a steadily drifting, non-repeatable reading. Use an ionizer or metal and glass containers.
• Handling with bare fingers. Moisture and grease add mass at the 0.1 mg level. Use tweezers or gloves.
• Magnetic samples. These interact with the force-restoration cell. Weigh them raised on a non-magnetic spacer, or use below-balance weighing if the model offers it.
• Adjusting with uncertified weights. This transfers the weight's own error directly into every reading. Adjust only with a weight of known, certified value.
• Undersized capacity. A 60 g sample in a heavy fixture can exceed the capacity of a smaller analytical balance. Size the capacity against the gross load, not the net load.

Frequently Asked Questions