Percentages & Proportions
Percentages in ordinary calculators are notoriously confusing. Standard calculators lack semantic context—pressing 100 + 10% on a pocket calculator might produce 100.1 instead of 110.
Kalc features a dedicated Percentage Engine with distinct AST node representations for direct scaling, additive markups, subtractive discounts, relative changes, and reverse percentage equations.
The 7 Core Percentage Patterns
| Pattern | Example Syntax | Mathematical Meaning | Evaluates To |
|---|---|---|---|
| 1. Direct Value | 20% of $150 | $\text{Base} \times (P / 100)$ | $30.00 |
| 2. Additive Markup | $50 + 10% or 10% on $50 | $\text{Base} \times (1 + P / 100)$ | $55.00 |
| 3. Subtractive Discount | $80 - 15% or 15% off $80 | $\text{Base} \times (1 - P / 100)$ | $68.00 |
| 4. Relative Change | $50 to $75 as % | $((B - A) / A) \times 100$ | 50% |
| 5. Proportional Ratio | $50 as a % of $200 | $(A / B) \times 100$ | 25% |
| 6. Proportional Markup | $70 as a % on $20 | $((A - B) / B) \times 100$ | 250% |
| 7. Proportional Discount | $20 as a % off $80 | $((B - A) / B) \times 100$ | 75% |
1. Direct Percentage (P% of Base)
Calculates the exact fraction of a number, currency, or physical dimension:
15% of $80 // $12.00
8.5% of $3,400 // $289.00
25% of 120 km // 30 km
33% of 2 hours in mins // 39.6 min2. Additive Percentages (Base + P% / P% on Base)
Adds a percentage to a base value. Kalc recognizes descriptive words like tip, tax, sales tax, markup, or bonus:
dinner = $75 + 20% tip // $90.00
subtotal $3,400 + 8.25% sales tax // $3,680.50
10% on $500 // $550.00
Wholesale $450 + 40% markup // $630.00
salary $120,000 + 15% bonus // $138,000.003. Subtractive Percentages (Base - P% / P% off Base)
Reduces a value by a specified percentage. Accepts descriptive terms like discount or off:
MSRP = $1,200 - 15% discount // $1,020.00
20% off $80 // $64.00
portfolio $500k - 8% market drawdown // $460,000.00
Weight 85 kg - 5% in kg // 80.75 kg4. Relative Change (A to B as %)
Calculates the rate of growth or reduction between two values:
50 to 90 as % // 80%
100 to 80 as % // -20%
$42k to $48.3k as % // 15%
line1 to line2 as % // Computes relative growth across lines5. Proportions & Ratios (as a % of / on / off)
A as a % of B
Calculates direct proportional share:
$50 as a % of $200 // 25%
Rent $2,400 as a % of Income $6,000 // 40%
35 min as a % of 1 hour // 58.33%A as a % on B
Calculates the markup of $A$ relative to cost $B$:
$70 as a % on $20 // 250%
Selling $35 as a % on Cost $10 // 250%A as a % off B
Calculates the effective discount of $A$ relative to original price $B$:
$20 as a % off $70 // 71.43%
Sale $120 as a % off Original $200 // 40%6. Reverse Percentage Equations
When budgeting or auditing invoices, you often know the final amount and need to calculate the pre-tax, pre-discount, or pre-fee origin.
Kalc solves these automatically using natural language:
P% of what is Target
Solves the initial base before a direct percentage was applied:
5% of what is 6 EUR // 120.00 EUR
Agent fee 6% of what is $24,000 // $400,000.00 (Property price)
Seed round 15% of what is $750k // $5,000,000.00 (Company valuation)P% on what is Target
Solves the original net price before sales tax or markup:
10% on what is $110 // $100.00
8.5% on what is $1,085 // $1,000.00
19% VAT on what is 1,428 EUR // 1,200.00 EUR (Pre-tax subtotal)P% off what is Target
Solves the original full sticker price before a discount was taken:
20% off what is $80 // $100.00
40% off what is sale tag $144 // $240.00 (Original MSRP)
15% rebate off what is $34,000 // $40,000.00