Cut and Fill Balance Calculator: equations, variables, units and worked solution

The cut and fill balance calculator calculates Usable loose cut, Loose fill demand, Material balance from Cut bank volume, Cut swell, Usable excavated material, Required compacted fill, Fill shrinkage. It does not hide the arithmetic: the result panel shows the governing formula, canonical-unit conversion, numeric substitution, unrounded evaluation and final rounded answer for every output.

Variables and measurement units

For the Cut and Fill Balance Calculator, Cut bank volume, Cut swell, and Usable excavated material are normalized to yd³, %, and % before cutBankVolume*(1+swell/100)*usablePercent/100 is evaluated. The unrounded value used for cutBankVolume*(1+swell/100)*usablePercent/100 and Usable loose cut is retained internally; formatting is applied only to the result cards.

Formula model

Cut is converted to usable loose material; fill is converted to required bank volume before comparison.

Formula-based worked derivation

1. Usable loose cut
   1. Formula: Usable loose cut = cutBankVolume × (1+swell ÷ 100) × usablePercent ÷ 100
   2. Default substitution: Usable loose cut = (1000) × (1+(20) ÷ 100) × (90) ÷ 100
   3. Unrounded evaluation: 1080 yd³
   4. Displayed answer: 1080 yd³
2. Loose fill demand
   1. Formula: Loose fill demand = fillCompactedVolume ÷ (1-shrinkage ÷ 100)
   2. Default substitution: Loose fill demand = (850) ÷ (1-(12) ÷ 100)
   3. Unrounded evaluation: 965.909090909 yd³
   4. Displayed answer: 965.91 yd³
3. Material balance
   1. Formula: Material balance = cutBankVolume × (1+swell ÷ 100) × usablePercent ÷ 100-fillCompactedVolume ÷ (1-shrinkage ÷ 100)
   2. Default substitution: Material balance = (1000) × (1+(20) ÷ 100) × (90) ÷ 100-(850) ÷ (1-(12) ÷ 100)
   3. Unrounded evaluation: 114.090909091 yd³
   4. Displayed answer: 114.09 yd³

In the Cut and Fill Balance Calculator, changing Cut bank volume, Cut swell, and Usable excavated material rebuilds the numeric substitution for cutBankVolume*(1+swell/100)*usablePercent/100. The engine converts selected measurements to yd³, %, and %, retains unrounded values, and, when reverse solving is available, inserts the solved variable back into the same equation to verify cutBankVolume*(1+swell/100)*usablePercent/100 and Usable loose cut with a numerical residual.

Input and output interpretation

Use measured or documented values for Cut bank volume, Cut swell, Usable excavated material, Required compacted fill, Fill shrinkage. The calculated outputs are Usable loose cut, Loose fill demand, Material balance. Check each intermediate line before relying on the final value; an implausible intermediate quantity usually identifies a unit, range or assumption error.

Algorithm and verification

The Cut and Fill Balance Calculator uses its own `cut-fill-balance` JavaScript engine to calculate cutBankVolume*(1+swell/100)*usablePercent/100 and Usable loose cut from Cut bank volume, Cut swell, and Usable excavated material with cutBankVolume*(1+swell/100)*usablePercent/100. Calculator-owned boundary and mode tests check that workflow; an external frozen-reference oracle checks the numeric outputs, and physical source mutation testing confirms that a changed `cut-fill-balance` engine is rejected.

Visual interpretation

In the Cut and Fill Balance Calculator, this guidance applies to Cut bank volume, Cut swell, and Usable excavated material and the reported cutBankVolume*(1+swell/100)*usablePercent/100 and Usable loose cut. The `cut-fill-balance` workflow evaluates cutBankVolume*(1+swell/100)*usablePercent/100 in yd³, %, and %; Verify local codes, product coverage and structural requirements before purchasing or construction.. Verification context: d73002.

Dimensional formula audit

The cut and fill balance calculator normalizes cutBankVolume (Cut bank volume, yd³), swell (Cut swell, %), usablePercent (Usable excavated material, %), fillCompactedVolume (Required compacted fill, yd³), shrinkage (Fill shrinkage, %) before evaluating the equations. Its reported quantities are Usable loose cut in yd³, Loose fill demand in yd³, Material balance in yd³. This separation matters because a numerical value without its measurement dimension can produce a plausible-looking but physically or financially incorrect answer. Conversion factors are applied before substitution, and output conversion occurs only after the canonical result has been calculated at full precision.

• Usable loose cut = cutBankVolume × (1+swell ÷ 100) × usablePercent ÷ 100
• Loose fill demand = fillCompactedVolume ÷ (1-shrinkage ÷ 100)
• Material balance = cutBankVolume × (1+swell ÷ 100) × usablePercent ÷ 100-fillCompactedVolume ÷ (1-shrinkage ÷ 100)

Formula sensitivity and boundary verification

To verify the cut and fill balance calculator, hold all other inputs fixed and change cutBankVolume within its permitted range. The live substitution line shows exactly where that value enters the equation for Usable loose cut. Repeat the check with swell. The result must follow the displayed algebra, remain finite, and retain the stated output unit. At minimum and maximum boundaries, the validator rejects undefined domains, impossible denominators and nonphysical values rather than silently returning a number.

Manual reproduction of the result

For an independent hand check, first convert every selected unit to the canonical units shown in the variable table. Next copy the governing equation, replace each symbol with the canonical value shown in the live derivation, and calculate the intermediate expression without early rounding. Finally round only once to the displayed precision and compare both the numerical value and unit with the calculator card. This process makes the cut and fill balance calculator reproducible instead of relying on an unexplained result.

Limitations

For the Cut and Fill Balance Calculator, Verify local codes, product coverage and structural requirements before purchasing or construction.. The calculator applies cutBankVolume*(1+swell/100)*usablePercent/100 to Cut bank volume, Cut swell, and Usable excavated material and reports cutBankVolume*(1+swell/100)*usablePercent/100 and Usable loose cut; confirm the real-world data, code, product specification, or professional standard before acting on a consequential result.