High-Low Method Calculator
From the highest and lowest activity and total cost, estimate the variable cost per unit, fixed cost and separate them — a quick cost-behaviour tool.
Input Data
Results
At a glance:The high-low method splits mixed cost (part fixed, part variable) into variable cost per unit and fixed cost using only the highest- and lowest-activity points. Variable cost per unit = (high cost − low cost) ÷ (high activity − low activity); fixed cost = high cost − variable cost × high activity (or low point). It assumes a linear cost line, so only two points are needed — fast for screening. Caveats: uses only two extremes, sensitive to outliers, ignores the rest; assumes linearity; for accuracy use regression. Still handy for quick estimates.
Formula
Variable cost per unit = (high cost − low cost) ÷ (high activity − low activity).
Fixed cost = high cost − variable cost × high activity.
$$VC_{\text{unit}} = \dfrac{\text{Cost}_{\text{high}} - \text{Cost}_{\text{low}}}{\text{Units}_{\text{high}} - \text{Units}_{\text{low}}}$$$$FC = \text{Cost}_{\text{high}} - VC_{\text{unit}} \times \text{Units}_{\text{high}}$$How to Use
- Enter the high-activity level and its total cost.
- Enter the low-activity level and its total cost.
- View the variable cost per unit and the fixed cost.
At high 1,200 / HK$22,000 and low 400 / HK$10,000
| Item | Value |
|---|---|
| Variable cost per unit | HK$15.00 |
| Fixed cost | HK$4,000 |
| Cost at 1,200 | 4,000 + 15 × 1,200 = 22,000 (matches) |
| Cost at 400 | 4,000 + 15 × 400 = 10,000 (matches) |
Variable cost = (22,000 − 10,000) ÷ (1,200 − 400) = 15; fixed = 22,000 − 15 × 1,200 = 4,000. Both points must fit the line.
Case Studies
Case 1: Split mixed cost
A workshop: highest month 1,200 units / HK$22,000; lowest 400 units / HK$10,000.
Variable cost per unit = (22,000 − 10,000) ÷ (1,200 − 400) = 12,000 ÷ 800 = HK$15; fixed cost = 22,000 − 15 × 1,200 = HK$4,000 (or 10,000 − 15 × 400 = 4,000, same).
So cost = 4,000 + 15 × units. For budgeting say 1,000 units: 4,000 + 15,000 = 19,000. Quick and easy, but only two points — if either month is unusual the result is off.
Case 2: Beware an outlier
Suppose the low point was an abnormal idle month (only 100 units / HK$9,000); high unchanged 1,200 / 22,000.
Variable = (22,000 − 9,000) ÷ (1,200 − 100) = 13,000 ÷ 1,100 ≈ 11.82; fixed = 22,000 − 11.82 × 1,200 ≈ 7,816 — far from the Case 1 split.
Lesson: the high-low result hinges entirely on those two extremes; one abnormal point moves it a lot. For reliable budgeting, screen outliers first or use regression on all data.
FAQ
Find variable and fixed cost from two points?
Pick the highest-activity and lowest-activity observations. Because cost = fixed + variable × activity, the difference between the two points is only variable cost changing with activity, so variable cost per unit = (high cost − low cost) ÷ (high activity − low activity). Then fixed cost = high cost − variable per unit × high activity (or the low point). The high-low method needs only two points, quick for screening.
Why use only two points?
The high-low method assumes cost changes linearly with activity, so the slope (variable cost per unit) is the same everywhere; any two points give the same line, and the extremes are the most spread, minimising rounding error. So only the highest and lowest are needed, not all data. Fast but crude.
When is it unreliable?
Two big flaws. (1) It uses only two points, ignoring everything in between, so if either extreme is an outlier (one-off large order, abnormal idle), the result is badly skewed. (2) It assumes linearity; if cost is stepped or curved (economies of scale), the straight-line split is wrong. For reliability, collect more points and use regression, or at least check with the mid-point.
High-low vs regression (least squares)?
Both split mixed cost, but differ in data use and accuracy. High-low uses only the highest and lowest points — fast, simple, no stats, but ignores all mid data, so outliers and non-linearity easily skew it; it is a screening/quick tool. Regression fits a line through ALL points by least squares — uses full data, less sensitive to single outliers, and yields R² for fit, far more reliable — but needs more data and computation. Practical: high-low for a fast first estimate and intuition; regression (or scatter + the mid-point check) when precision matters (budgeting, pricing, decisions). High-low's role is speed, not accuracy.
High-low vs scatter-graph and account analysis?
Three common ways to split mixed cost, each with a role. (1) Scatter-graph: plot all (activity, cost) points, eyeball/visually fit a line — intuitive, reveals outliers and non-linearity high-low misses, but subjective. (2) High-low: pick the two extremes, compute slope and intercept — fast, objective, but uses only two points, outlier-sensitive. (3) Account analysis: rely on accounting knowledge to classify each cost as fixed/variable/semi — no formula, depends on judgement and records, practical for known cost structures. Choose: rough quick estimate → high-low; check pattern and outliers → scatter-graph; known structure → account analysis; most accurate → regression. High-low is the fastest first pass, not the final word.
Related Tools
References
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.