Calculation Methodology
Algebraic proofs, metric definitions, float protections, precision standards, and validation protocols behind every SeeCalc calculator.
Verified Proofs
Every formula is derived from first principles and cross-checked algebraically.
7 Spec Sections
Covering float safety, precision, definitions, coverage, validation, and QA.
Industry-Standard
All metric definitions follow IAB, MMA, and SaaS industry accepted standards.
Section 01
Floating Point Guards & Division-by-Zero Protection
JavaScript/TypeScript numbers are double-precision binary floats (IEEE 754). Without guards, dividing by zero returns Infinity or NaN, causing layout crashes or silently wrong outputs.
Guard Type
Non-zero denominator check before every division operation.
Safe Return
Returns structured zero object — never throws, never renders NaN.
UI Signal
Red inline warning text is surfaced to the user when inputs are invalid.
TypeScript — CPM Guard Implementation
// Guard: impressions must be a positive number
if (!impressions || impressions <= 0) {
return { cpm: 0, perImpression: 0 };
}
// Guard: cost must be non-negative
if (cost < 0) {
return { cpm: 0, perImpression: 0 };
}
const cpm = (cost / impressions) * 1000;
const perImpression = cost / impressions;
return { cpm, perImpression };This pattern is applied uniformly across every solver function. The return shape is always typed — no undefined values propagate to the UI layer.
Section 02
Algebraic Multi-Way Reverse Solving
Traditional marketing tools are strictly one-directional. SeeCalc derives all rearrangements of each formula algebraically so every variable is solvable — not just the canonical output.
Example: CPM — All Three Directions
CPM = (Cost ÷ Imp) × 1000
Standard forward direction
Cost = (Imp × CPM) ÷ 1000
Given target CPM + impressions
Imp = (Cost ÷ CPM) × 1000
Given budget + target CPM
Example: ROAS — All Three Directions
ROAS = Revenue ÷ AdSpend
Standard forward direction
Revenue = ROAS × AdSpend
Given target ROAS + budget
AdSpend = Revenue ÷ ROAS
Given revenue target + ROAS goal
All derivations are verified to be mathematically reciprocal — substituting any solved value back into the base formula returns the original inputs exactly (subject only to float precision bounds defined in Section 03).
Section 03
Numeric Precision & Rounding Standards
Raw float arithmetic produces trailing precision noise (e.g. 0.1 + 0.2 === 0.30000000000000004). Each metric category applies a fixed rounding rule at the display layer without altering intermediate computation.
| Metric Category | Decimal Places | Rounding Method | Example Output |
|---|---|---|---|
| Currency (CPM, CPA, CPC) | 2 | Half-up | $12.47 |
| Rate / Ratio (CTR, CVR, Churn) | 2–4 | Half-up | 3.82% |
| ROAS / ROI multiplier | 2 | Half-up | 4.15× |
| Integer counts (Impressions) | 0 | Floor | 1,240,000 |
| LTV / Revenue projections | 2 | Half-up | $284.60 |
| Percentage margins | 1 | Half-up | 67.3% |
Rounding is applied only at the display boundary (toFixed / Intl.NumberFormat). All intermediate calculations retain full float precision to prevent compounding rounding error across chained formulas.
Section 04
Metric Definition Registry
All metric definitions follow IAB (Interactive Advertising Bureau), MMA Global, and common SaaS industry standards. Definitions are pinned — they do not change based on platform, campaign type, or geography.
Formula
(Ad Spend ÷ Impressions) × 1000Definition
The cost an advertiser pays per 1,000 ad impressions served. Standard unit for display and programmatic buying.
Formula
Ad Spend ÷ ClicksDefinition
Total spend divided by the number of ad clicks received. Primary metric for search and performance campaigns.
Formula
(Clicks ÷ Impressions) × 100Definition
The percentage of impressions that result in a user click. Expressed as a percentage.
Formula
Revenue ÷ Ad SpendDefinition
Revenue generated per dollar of ad spend. A multiplier: ROAS of 4 means $4 returned per $1 spent.
Formula
Ad Spend ÷ ConversionsDefinition
The cost to acquire one converting customer or completed action. Also called Cost Per Conversion.
Formula
(Conversions ÷ Clicks) × 100Definition
Percentage of clicks that result in a defined conversion event (purchase, signup, form fill, etc.).
Formula
ARPU × Gross Margin ÷ Churn RateDefinition
Predicted total revenue a customer generates over their full relationship with the business.
Formula
Total Sales & Marketing Spend ÷ New CustomersDefinition
Total cost to acquire one new paying customer, including all sales and marketing expenses.
Formula
Active Customers × Average Monthly RevenueDefinition
Predictable, normalized monthly revenue from all active subscriptions.
Formula
(Customers Lost ÷ Customers at Start) × 100Definition
Percentage of customers who cancel or do not renew within a given period.
Section 05
Input Validation Protocol
All user inputs pass through a staged validation pipeline before reaching any solver function. Validation is non-blocking — invalid inputs surface contextual error text rather than preventing further interaction.
Stage 1 · Type Check
Input is parsed through parseFloat(). Non-numeric strings (letters, symbols) return NaN and are caught immediately.
Stage 2 · Range Check
Values are tested against domain constraints: percentages must be 0–100, rates must be ≥ 0, denominators must be > 0.
Stage 3 · Coherence Check
Inter-field relationships are validated: Clicks cannot exceed Impressions; Conversions cannot exceed Clicks.
Stage 4 · Solver Gate
Only after all three checks pass does the solver execute. Partial passes return partial results with inline warnings.
Section 06
Edge Case Handling
Marketing data frequently contains values that are technically valid inputs but produce mathematically degenerate results. Each edge case below has a defined handling contract.
| Edge Case | Affected Metric | Handling Contract |
|---|---|---|
| 0 impressions with non-zero spend | CPM, CTR | Return 0. Display: 'Impressions must be greater than zero.' |
| CTR > 100% | CTR | Flag as incoherent. Warn: 'Clicks cannot exceed Impressions.' |
| 100% churn rate | LTV, MRR retention | LTV returns 0 (no customer survives). Warning shown. |
| Negative ad spend | All spend-based metrics | Treat as invalid. Return 0 with type error warning. |
| ROAS < 1× | ROAS, Profit | Valid — a losing campaign. No warning. Result displayed normally. |
| CAC > LTV | LTV:CAC ratio | Valid and common. Ratio displayed; no correction applied. |
| CVR > 100% | CVR | Flag as incoherent. Warn: 'Conversions cannot exceed Clicks.' |
| Churn rate of 0% | Churn, LTV | LTV approaches infinity. Cap display and note infinite retention. |
Section 07
Quality Assurance & Verification Process
Every formula on SeeCalc passes a four-stage review before deployment. No calculator ships without completing all four stages.
Algebraic Derivation Review
Each formula and all its reverse derivations are written out in symbolic notation and verified by hand before any code is written. Derivations are checked for mathematical equivalence and completeness.
Reference Cross-Check
The formula definition is compared against at least two independent authoritative sources (IAB standards, MMA Global guidelines, academic marketing textbooks, or platform documentation from Google Ads / Meta).
Known-Value Smoke Tests
Each solver function is run against a set of manually calculated known-value pairs (e.g. cost=$500, impressions=100,000 → CPM=$5.00). Any discrepancy fails the calculator.
Edge Case Regression Suite
All edge cases defined in Section 06 are run against every relevant calculator. New edge cases discovered during production are immediately added to the suite and used to regression-test all affected calculators.
Methodology Integrity Commitment
If you identify an error in any formula, definition, or edge case contract on this page, contact us at info@seecalc.com. Formula errors are treated as critical bugs — reviewed and corrected within one business day.