Arc Skills / Architecture and engineering budgets
Check units and dimensions in engineering calculations
Unit checking catches impossible arithmetic before a number enters a budget or verification report. Arc Skills takes original expressions and declared units and returns a dimension trace plus a proposed correction where intent is clear.
Use this skill
Use Arc Skills to audit units and dimensions in my engineering equations.
Inputs:
- Original expressions, variable values, declared units, and source revision
- Expected output quantities and physical meaning of each term
- Any absolute-temperature, interval, angular, or reference-frame conventions
Return the original expression, term-by-term dimension trace, result or failure, and a proposed correction only where the physical intent is supported. Keep dimensional validity separate from model validity.What you provide and what you get
| What you have | How it is used | What you get |
|---|---|---|
| Original expressions | Keeps errors traceable to source text | Pass/fail row per equation |
| Variable units and expected quantity | Determines operation validity | Dimension trace and corrected unit |
| Temperature meaning | Separates offset values from intervals | Correct conversion or open intent |
Energy multiplication passes; addition fails
Illustrative engineering example.
Assume a device draws 12 W for 30 s. A second calculation adds those two numbers, while a thermal comparison asks for the difference between 30 °C and 20 °C.
E₁ = 12 W × 30 s
E₂ = 12 W + 30 s
ΔT = 30 °C − 20 °C| Expression | Dimension trace | Result | Finding |
|---|---|---|---|
| 12 W × 30 s | W × s = J | 360 J | Valid energy calculation if power is constant over interval |
| 12 W + 30 s | power + time | No defined sum | Invalid; addition needs compatible dimensions |
| 30 °C − 20 °C | absolute temperature subtraction | 10 °C = 10 K interval | Valid difference; no 273.15 offset |
| 30 °C absolute in K | 30 + 273.15 | 303.15 K | Offset applies to absolute temperature |
The correction for the second row is multiplication only if the source really intends energy consumed at constant 12 W over 30 s. Otherwise the intended model is unresolved; unit consistency alone cannot infer the physics. A dimensionally valid force divided by area likewise says nothing about whether the chosen force is the governing load.
The temperature example illustrates why an interval and an absolute reading need different conversion rules. NIST states that a 1 °C temperature interval has the same magnitude as 1 K, while Celsius absolute values require an offset to kelvin.
Run a short unit audit
- Inventory each variable with its authored value, unit and physical meaning.
- Reduce every term to base dimensions and reject addition of unlike dimensions.
- Convert compatible units before arithmetic and distinguish absolute from difference quantities.
- Check whether the equation represents the intended physical relationship after dimensions pass.
Questions about this task
Does correct dimensional form prove the answer?
No. It catches one class of error; boundary conditions, chosen variables and the physical model still need engineering review.
When do I add 273.15?
When converting an absolute Celsius temperature to kelvin. Do not add it to a temperature difference.
Sources and further reading
- NIST Guide to the SI: Chapter 8: Physical units and the distinction between temperature values and intervals.
- NASA Systems Engineering Handbook: appendix: Terminology for budgets, margin and technical resources.