manufacturing.variance
Standard costing variances: material price and usage, labour rate and efficiency, favourable or adverse.
1.0.0 · published 2026-10-03 by charlie · Anterra
Pinned by 15 tests, run in TypeScript, Python and Rust.
What it does
The four basic standard-costing variances for a period, flexed to the output actually produced:
material price = actual material cost - AQ x SP material usage = (AQ - SQ) x SP SQ = standard quantity per unit x actual output labour rate = actual labour cost - AH x SR labour efficiency = (AH - SH) x SR SH = standard hours per unit x actual output
For example
cost_variances(standard price £3.00, standard quantity …, actual quantity …, actual cost £6,160.00, standard rate £10.00, standard hours …, actual hours …, actual cost £30,450.00, 1,000, half-up)→ material price …, material usage …, labour rate …, labour efficiency …, total …, standard cost £36,000.00, actual cost £36,610.00 the textbook case: 2 kg at £3 and 3 h at £10 a unit, 1000 made with 2200 kg for £6160 and 2900 h for £30450cost_variances(standard price £1.25, standard quantity …, actual quantity …, actual cost £42.00, standard rate £11.50, standard hours …, actual hours …, actual cost £300.00, 100, half-up)→ material price …, material usage …, labour rate …, labour efficiency …, total …, standard cost £329.17, actual cost £342.00 fractional standards: 1/3 kg at £1.25 and 1/4 h at £11.50 a unit, 100 made using 33.5 kg; each flexed cost is rounded once and the variances still add upcost_variances(standard price £1.25, standard quantity …, actual quantity …, actual cost £42.00, standard rate £11.50, standard hours …, actual hours …, actual cost £300.00, 100, down)→ material price …, material usage …, labour rate …, labour efficiency …, total …, standard cost £329.16, actual cost £342.00 the same rounded down: 4187.5p and 4166.67p become 4187p and 4166p
The function
The same function in TypeScript, Python and Rust, pinned by the same tests. Pick your language; the choice follows you around the registry.
def cost_variances(material: MaterialActual, labour: LabourActual, actual_output: int, mode: RoundingMode) -> CostVariances| material | MaterialActual | standard and actual material for the period |
| labour | LabourActual | standard and actual labour for the period |
| actual_output | int | units actually produced, which the standard is flexed to |
| mode | RoundingMode | how each flexed cost becomes whole minor units |
| returns | CostVariances |
The types it declares, generated into your project
@dataclass(frozen=True)
class MaterialActual:
"""Material standard per unit of output, and what was actually used and paid."""
#: per unit of material (per kg, per metre)
standard_price: Money
#: material per unit of output
standard_quantity: Rational
#: material actually used
actual_quantity: Rational
#: what the material used actually cost
actual_cost: Money
@dataclass(frozen=True)
class LabourActual:
"""Labour standard per unit of output, and what was actually worked and paid."""
#: per hour
standard_rate: Money
#: hours per unit of output
standard_hours: Rational
#: hours actually worked
actual_hours: Rational
#: what those hours actually cost
actual_cost: Money
@dataclass(frozen=True)
class Variance:
"""One variance: how big, and which way."""
#: never negative
amount: Money
effect: VarianceEffect
VarianceEffect = Literal["favourable", "adverse", "none"]
@dataclass(frozen=True)
class CostVariances:
"""The four variances, their total, and the costs they reconcile."""
#: actual cost - actual quantity x standard price
material_price: Variance
#: (actual quantity - standard quantity for actual output) x standard price
material_usage: Variance
#: actual cost - actual hours x standard rate
labour_rate: Variance
#: (actual hours - standard hours for actual output) x standard rate
labour_efficiency: Variance
#: actualCost - standardCost; always the sum of the four
total: Variance
#: standard material and labour for the actual output
standard_cost: Money
#: actual material and labour cost
actual_cost: MoneyYour code names it in one line, in the file that uses it
from fune.manufacturing.variance import cost_variances # manufacturing.variance@^1Imports name this capability’s declared dependencies, which fune builds next to it in your project; each one links to its page.
from .manufacturing_variance_types import CostVariances, LabourActual, MaterialActual, Variance
from .math_rational import Rational, multiply_rational, rational, rational_to_integer ← from math.rational ^1.0.0 · built alongside by fune
from .math_round_div import RoundingMode ← from math.round-div ^1.0.0 · built alongside by fune
from .money_amount import Money, assert_same_currency, money ← from money.amount ^1.0.0 · built alongside by fune
MAX_SAFE = 2**53 - 1
def _not_negative(name: str, value: Rational) -> Rational:
r = rational(value.numerator, value.denominator)
if r.numerator < 0:
raise ValueError("%s must not be negative" % (name,))
return r
def _cost_of(name: str, value: Money, unit: Money) -> int:
assert_same_currency(unit, value)
if value.minor < 0:
raise ValueError("%s must not be negative, received %d" % (name, value.minor))
return value.minor
def _variance(signed: int, currency: str) -> Variance:
effect = "adverse" if signed > 0 else "favourable" if signed < 0 else "none"
return Variance(amount=money(abs(signed), currency), effect=effect)
def cost_variances(material: MaterialActual, labour: LabourActual, actual_output: int, mode: RoundingMode) -> CostVariances:
"""Material price and usage, labour rate and efficiency variances, flexed
to actual output. The four flexed costs are each rounded once and every
variance is a difference of them, so the variances always sum exactly.
"""
if isinstance(actual_output, bool) or not isinstance(actual_output, int) or actual_output < 0 or actual_output > MAX_SAFE:
raise ValueError("actualOutput must be a whole number, not negative, received %r" % (actual_output,))
unit = material.standard_price
currency = unit.currency
sp = _cost_of("material standardPrice", material.standard_price, unit)
mat_actual = _cost_of("material actualCost", material.actual_cost, unit)
sr = _cost_of("labour standardRate", labour.standard_rate, unit)
lab_actual = _cost_of("labour actualCost", labour.actual_cost, unit)
sq = _not_negative("material standardQuantity", material.standard_quantity)
aq = _not_negative("material actualQuantity", material.actual_quantity)
sh = _not_negative("labour standardHours", labour.standard_hours)
ah = _not_negative("labour actualHours", labour.actual_hours)
output = rational(actual_output, 1)
actual_at_standard = rational_to_integer(multiply_rational(aq, rational(sp, 1)), mode)
standard_material = rational_to_integer(multiply_rational(multiply_rational(sq, output), rational(sp, 1)), mode)
hours_at_standard = rational_to_integer(multiply_rational(ah, rational(sr, 1)), mode)
standard_labour = rational_to_integer(multiply_rational(multiply_rational(sh, output), rational(sr, 1)), mode)
standard_cost = standard_material + standard_labour
actual_cost = mat_actual + lab_actual
return CostVariances(
material_price=_variance(mat_actual - actual_at_standard, currency),
material_usage=_variance(actual_at_standard - standard_material, currency),
labour_rate=_variance(lab_actual - hours_at_standard, currency),
labour_efficiency=_variance(hours_at_standard - standard_labour, currency),
total=_variance(actual_cost - standard_cost, currency),
standard_cost=money(standard_cost, currency),
actual_cost=money(actual_cost, currency),
)Install
fune buildWith that line in your source, in a Python project (language python in fune.project), fune build resolves it and its 3 dependencies, pins them in fune.lock, downloads only the Python package of each, and builds the code above into your project’s .fune/build, one readable file per capability with a header linking back here. Or pin a range in fune.project and build in one step:
fune add manufacturing.varianceThe manifest, vectors and README with only the Python implementation. Install it without the registry with fune add ./manufacturing.variance-1.0.0-python.fune, or fetch it from a terminal with fune pull manufacturing.variance@1.0.0:python.
The whole function, every language, is one file too: manufacturing.variance-1.0.0.fune, 33,167 bytes, sha256 891beb9988a990d3a686a6a4e0993bc51814dd5d685d087f0e5ebdcb2c68455c. It installs into a project of any language.
Customise it in your app
The seams this capability offers. Put a marker directly above a function of your own and fune build wires it into the built code; the package on the registry is not changed, the built file’s header lists it under CUSTOMISED, and fune hooks lists every hook in the project. How hooks work.
before — your function gets the arguments and returns them, changed or not, or throws to refuse the call.
# fune: before manufacturing.varianceafter — your function gets the result and the arguments, and returns the final result.
# fune: after manufacturing.variancereplace — inside this capability’s code only, calls to a dependency go to your function, with the same signature. Other capabilities that use it are unaffected; write in * to replace it everywhere.
# fune: replace math.rational in manufacturing.variance
# fune: replace math.round-div in manufacturing.variance
# fune: replace money.amount in manufacturing.variancestep — your function runs at a numbered point inside the function’s body, receives the in-scope values it names as parameters, and may return replacements. List the points with fune show manufacturing.variance --steps.
# fune: step manufacturing.variance after <n|label>Tests
A version published now needs at least 8 tests for every function, and one that expects the error for each function that throws; the registry refuses it otherwise. fune verify --all runs each case in TypeScript, Python and Rust, and a project runs them again with fune verify. This page lists the cases; it does not run them. The exact JSON is vectors.json.
| Case | Arguments | Expected | |
|---|---|---|---|
| the textbook case: 2 kg at £3 and 3 h at £10 a unit, 1000 made with 2200 kg for £6160 and 2900 h for £30450 | standard price £3.00, standard quantity …, actual quantity …, actual cost £6,160.00, standard rate £10.00, standard hours …, actual hours …, actual cost £30,450.00, 1,000, half-up | → | material price …, material usage …, labour rate …, labour efficiency …, total …, standard cost £36,000.00, actual cost £36,610.00 |
| fractional standards: 1/3 kg at £1.25 and 1/4 h at £11.50 a unit, 100 made using 33.5 kg; each flexed cost is rounded once and the variances still add up | standard price £1.25, standard quantity …, actual quantity …, actual cost £42.00, standard rate £11.50, standard hours …, actual hours …, actual cost £300.00, 100, half-up | → | material price …, material usage …, labour rate …, labour efficiency …, total …, standard cost £329.17, actual cost £342.00 |
| the same rounded down: 4187.5p and 4166.67p become 4187p and 4166p | standard price £1.25, standard quantity …, actual quantity …, actual cost £42.00, standard rate £11.50, standard hours …, actual hours …, actual cost £300.00, 100, down | → | material price …, material usage …, labour rate …, labour efficiency …, total …, standard cost £329.16, actual cost £342.00 |
| exactly on standard: every variance is none | standard price £5.00, standard quantity …, actual quantity …, actual cost £50.00, standard rate £20.00, standard hours …, actual hours …, actual cost £100.00, 10, half-up | → | material price …, material usage …, labour rate …, labour efficiency …, total …, standard cost £150.00, actual cost £150.00 |
| nothing made: everything used is usage and efficiency variance | standard price £5.00, standard quantity …, actual quantity …, actual cost £20.00, standard rate £20.00, standard hours …, actual hours …, actual cost £40.00, 0, half-up | → | material price …, material usage …, labour rate …, labour efficiency …, total …, standard cost £0.00, actual cost £60.00 |
| dear material used sparingly and cheap labour working fast: favourable overall | standard price £3.00, standard quantity …, actual quantity …, actual cost £6,045.00, standard rate £10.00, standard hours …, actual hours …, actual cost £27,440.00, 1,000, half-up | → | material price …, material usage …, labour rate …, labour efficiency …, total …, standard cost £36,000.00, actual cost £33,485.00 |
| hours in minutes as a fraction: 90 minutes is 3/2 hours | standard price €10.00, standard quantity …, actual quantity …, actual cost €10.00, standard rate €24.00, standard hours …, actual hours …, actual cost €36.00, 1, half-up | → | material price …, material usage …, labour rate …, labour efficiency …, total …, standard cost €34.00, actual cost €46.00 |
| costs in two currencies are an error | standard price £3.00, standard quantity …, actual quantity …, actual cost £6,160.00, standard rate €10.00, standard hours …, actual hours …, actual cost €30,450.00, 1,000, half-up | → | error: currency mismatch |
| negative output is an error | standard price £3.00, standard quantity …, actual quantity …, actual cost £6,160.00, standard rate £10.00, standard hours …, actual hours …, actual cost £30,450.00, -1, half-up | → | error: actualOutput must be a whole number, not negative |
| fractional output is an error | standard price £3.00, standard quantity …, actual quantity …, actual cost £6,160.00, standard rate £10.00, standard hours …, actual hours …, actual cost £30,450.00, 2.5, half-up | → | error: actualOutput must be a whole number, not negative |
Show the other 5 tests
| Case | Arguments | Expected | |
|---|---|---|---|
| a negative actual quantity is an error | standard price £3.00, standard quantity …, actual quantity …, actual cost £6,160.00, standard rate £10.00, standard hours …, actual hours …, actual cost £30,450.00, 1,000, half-up | → | error: material actualQuantity must not be negative |
| negative standard hours are an error | standard price £3.00, standard quantity …, actual quantity …, actual cost £6,160.00, standard rate £10.00, standard hours …, actual hours …, actual cost £30,450.00, 1,000, half-up | → | error: labour standardHours must not be negative |
| a negative standard price is an error | standard price -£3.00, standard quantity …, actual quantity …, actual cost £6,160.00, standard rate £10.00, standard hours …, actual hours …, actual cost £30,450.00, 1,000, half… | → | error: material standardPrice must not be negative |
| a negative actual labour cost is an error | standard price £3.00, standard quantity …, actual quantity …, actual cost £6,160.00, standard rate £10.00, standard hours …, actual hours …, actual cost -£0.01, 1,000, half-up | → | error: labour actualCost must not be negative |
| a zero denominator is an error | standard price £3.00, standard quantity …, actual quantity …, actual cost £6,160.00, standard rate £10.00, standard hours …, actual hours …, actual cost £30,450.00, 1,000, half-up | → | error: denominator must not be zero |
More from the author
A variance is **adverse** when actual cost is higher than standard and **favourable** when it is lower; `amount` is always the size and `effect` the direction (`none` for exactly zero). The textbook case: a standard of 2 kg at £3/kg and 3 hours at £10/h, 1,000 units made using 2,200 kg for £6,160 and 2,900 hours for £30,450, gives material price £440 F, usage £600 A, labour rate £1,450 A, efficiency £1,000 F, and £610 A in total.
**The variances always add up.** Quantities and hours are exact fractions (`Rational`: 1/3 kg, 1/4 hour), so the flexed costs (AQ x SP, SQ x SP, AH x SR, SH x SR) are exact fractions of a minor unit. Each of those four is rounded once by `mode`, and every variance is a difference of whole amounts, so price plus usage is exactly actual material cost less standard material cost, and the four together are exactly `actualCost - standardCost`. Rounding each variance on its own would leave a penny or two unexplained.
**Price variance on usage.** The material price variance is computed on the quantity used, not the quantity purchased; where stock is held at standard cost and the price variance is taken on purchase, pass purchases in a separate call with the purchase quantity as `actualQuantity`.
**Rules.** All money must be in the currency of `material.standardPrice`. Prices, rates, quantities, hours and costs may not be negative; output is a whole number, not negative. With zero output, all material and labour used is usage and efficiency variance. Overhead variances are not included.
Source: CIMA Official Terminology (2005), "variance" entries for direct material price, direct material usage, direct labour rate and direct labour efficiency variances; the same definitions appear in ACCA Performance Management (PM) study material on standard costing.
Files
| Path | Bytes |
|---|---|
| README.md | 2,242 |
| impl/python.py | 3,284 |
| impl/rust.rs | 5,042 |
| impl/typescript.ts | 3,265 |
| vectors.json | 12,134 |