The range follows your entered bounds and a rectangular shape. It cannot establish whether those bounds contain the actual dimensions.
Define one rectangular space
Identify the same internal or external faces for length, width and height. Record units, location, date, instrument and method. Use safely accessible measurements or reviewed drawings; do not enter a tank or excavation to obtain a dimension.
This model needs a rectangular shape. Slopes, curved walls, varying depth and solid obstructions need separate geometry and quantities. Combining minimum widths taken at different locations does not turn an irregular space into a rectangle.
Document the bounds, not just repeated readings
Enter a justified lower and upper bound for each dimension. The minimum and maximum of a few repeat readings are only observed spread, not proof that the actual value is inside. Investigate alignment, reference faces and instrument information instead of assigning a convenient ± value.
NIST distinguishes repeatability, measurement error and uncertainty; they are not interchangeable. This calculator evaluates chosen scenarios, not an uncertainty budget or confidence interval.
NIST TN 1297 Appendix D1: measurement terminology (English; not dimensional tolerances) ↗Multiply matching endpoints
For positive dimensions the product grows with each dimension: multiply the three lower bounds for Vlo and the three upper bounds for Vhi. No statistical independence assumption is needed for this conditional envelope. Constraints between dimensions can make the envelope wider than physically attainable.
Example: 3.98–4.02 m × 2.98–3.02 m × 2.49–2.51 m gives 29.532396–30.472404 m³; difference 0.940008 m³. The midpoint dimensions give 30 m³, not the midpoint of the endpoint volumes (30.0024 m³), and neither is an expected value.
Use the range to decide what to measure again
Keep the six inputs and their basis with the result. If the range changes a purchase decision, improve the relevant measurements or geometry before choosing an order. The upper endpoint is not automatically the correct order quantity.
Equal bounds are accepted and give zero range when all three pairs are equal. That means fixed input assumptions, not perfect measurement. Material state, supplier yield, unusable space and any explicit allowance remain separate decisions.
A compact dimension record
| Record | Include | Do not infer |
|---|---|---|
| Each axis | Lower and upper metres; same faces | A bound from scale spacing alone |
| Evidence | Method, instrument, date and source | Calibration from repeat agreement |
| Result | Vlo, Vhi and difference in m³ | Confidence level or exact capacity |
Worked example
Fictional dimensional scenarios
A rectangular space has entered length bounds 3.98–4.02 m, width 2.98–3.02 m and height 2.49–2.51 m. These are example assumptions, not a measuring-device accuracy claim.
Vlo = 3.980000 × 2.980000 × 2.490000 = 29.532396 m³ Vhi = 4.020000 × 3.020000 × 2.510000 = 30.472404 m³ ΔV = 30.472404 − 29.532396 = 0.940008 m³
The conditional range is 29.532396–30.472404 m³. Keep the inputs; do not report it as a certified capacity or add an unexplained reserve.
What to have ready
- Same rectangular faces and units identified
- Six bounds and their justification recorded
- Upper bound at least equal to lower on each axis
- Shape limitations and obstructions checked separately
- Result and any procurement allowance kept separate
Common mistakes
- Calling repeated extrema guaranteed true bounds.
- Entering millimetres into metre fields.
- Multiplying a lower length by upper width and height as the minimum.
- Calling a zero range perfect measurement.
- Treating the upper volume as an approved order.
Use and limitations. Sources include US public agencies. Principles are general; regulations and design values must be checked where you live.Worked examples use stated hypothetical inputs.