measurement method

coin density verification by displaced water weight

authentic home calculator certificates coin archive

purpose

This method is used to estimate the material consistency of a coin by comparing its measured density against the expected density of the claimed material.

The primary method used by authentic.cosigo.io is water displacement by measured water mass. This is preferred over pure dimension-based geometry because real coins are not perfect cylinders.

core principle

Measured Density = Coin Mass ÷ Displaced Volume

When displaced water is weighed instead of read from a graduated cylinder, displaced volume is estimated from water mass.

Displaced Volume = Displaced Water Mass ÷ Water Density

Measured Density = Coin Mass ÷ Displaced Volume

For normal room-temperature testing, water density is close to 1 g/mL, but a temperature correction improves precision.

required equipment

Required

  1. Calibrated digital scale
  2. Coin to be measured
  3. Water container or overflow setup
  4. Secondary container for collecting displaced water
  5. Clean room-temperature water

Recommended

  1. Thermometer for water temperature
  2. Soft non-reactive handling method
  3. Stable work surface
  4. Repeat measurements for averaging

procedure

1. weigh the dry coin

Measure the coin mass in grams on a calibrated digital scale. Record only the coin mass. Do not include capsule, tray, holder, or support thread.

2. prepare the displacement setup

Prepare the water container so that displacement can be measured consistently. If using overflow collection, make sure the collection vessel is clean and tared before measurement.

3. measure water temperature

Record the water temperature in °C when possible. Temperature correction is small, but improves consistency.

4. submerge the coin slowly

Fully submerge the coin without trapping visible air bubbles. Avoid splashing and avoid allowing the coin to rest against the container wall if that changes the collection behavior.

5. collect and weigh displaced water

Collect the displaced water and weigh only the displaced water mass in grams. This is the primary measurement input for the calculator.

6. record optional before / after levels

If using a graduated cylinder, initial and final water levels may also be recorded. This is secondary to direct displaced-water mass when both are available.

7. record dimensions as cross-check only

Diameter and thickness may be recorded for an idealized geometry comparison. This is not the primary verification basis.

why displacement is primary

Water displacement

Measures the actual physical volume of the coin, including the real shape, relief, rim, and wear.

Geometry cross-check

Treats the coin as an ideal cylinder or rectangular solid. This is only an approximation.

A struck coin is not a perfect cylinder. Raised rims, design relief, local thickness variation, and wear make pure geometry less reliable for material verification.

sources of error

Common causes of bad results

  1. Air bubbles attached to the coin
  2. Water lost during transfer
  3. Water clinging to coin or container lip
  4. Incomplete submersion
  5. Incorrect tare
  6. Including holder or support in mass
  7. Scale instability or poor calibration

Good practice

  1. Repeat test multiple times
  2. Use consistent collection method
  3. Average repeated measurements
  4. Record temperature
  5. Handle coin carefully and consistently

interpreting results

Primary test: compare measured density from water displacement to expected density for the claimed material.

Cross-check: compare idealized geometry density only as an approximate secondary reference.

A close match between measured displacement density and expected material density supports the claimed composition. A large mismatch suggests re-testing or further examination.

The geometry estimate may differ significantly from displacement density without implying a material problem. This is normal for real coins.

tolerance guidance

A tolerance of about ±2.5% is a practical operational threshold for careful manual testing. Stricter thresholds may be possible with disciplined repeat measurements and a stable setup.

The most important comparison is:

Measured Density (water displacement) vs Expected Density (claimed material)

summary

authentic.cosigo.io uses displaced-water mass as the primary volume measurement because it reflects the actual physical volume of the tested coin. Dimensions are recorded only as an approximate geometry cross-check.

Certificate records should clearly distinguish:

Primary Material Verification

Dimension Cross-Check Only (Approximate)

This separation reduces confusion and makes the verification method easier to understand for non-technical readers.