Three calculations come up constantly for anyone running a small business or evaluating a purchase decision: was it worth it (ROI), what do I actually bill (invoice total), and how do I handle sales tax correctly. Here's the math for each, done right.
ROI: was it worth it?
Worked example: a $2,000 investment that grows to $2,500:
| Step | Calculation | Result |
|---|---|---|
| Gain | 2,500 − 2,000 | $500 |
| ROI | 500 ÷ 2,000 × 100 | 25% |
ROI works the same way for a loss — a $1,000 investment that drops to $850 has a gain of −$150, for an ROI of −15%. A negative ROI simply means the final value was lower than what went in.
What ROI doesn't account for: time. A 25% return over one year and a 25% return over five years are very different outcomes, but the raw ROI percentage looks identical — for comparing investments over different time periods, an annualized return figure is more meaningful than raw ROI alone.
Invoices: discount before tax, always
The order of operations matters here, and it's a common point of confusion: standard invoicing practice applies any discount to the subtotal first, then calculates tax on the already-discounted amount — not on the original subtotal.
Worked example: a $500 subtotal, 10% discount, 8% tax:
| Step | Calculation | Result |
|---|---|---|
| Discount amount | 500 × 10% | $50 |
| Discounted subtotal | 500 − 50 | $450 |
| Tax | 450 × 8% | $36 |
| Total | 450 + 36 | $486 |
Calculating tax on the original $500 subtotal instead (giving $40 tax and a $490 total) is a common but incorrect approach — most jurisdictions calculate sales tax on the actual amount being paid, which is the post-discount price.
Sales tax: adding vs. removing
Sales tax calculations run in two directions, and mixing them up is a frequent source of small errors.
Worked example (7% tax rate):
| Direction | Input | Calculation | Result |
|---|---|---|---|
| Adding tax | $80 price | 80 × 1.07 | $85.60 total |
| Removing tax | $85.60 total | 85.60 ÷ 1.07 | $80.00 pre-tax price |
Common mistake: to find the pre-tax price from a tax-inclusive total, people often just subtract the tax percentage directly (85.60 × 0.93 = $79.61) instead of dividing by (1 + rate). This gives a slightly wrong answer — subtracting a percentage and dividing by (1 + that percentage) are not the same operation, and the gap grows with higher tax rates.
Try the calculators
Each of these has a dedicated calculator: the ROI calculator, the invoice calculator (which applies discount before tax automatically), and the sales tax calculator for both adding and removing tax.
Frequently asked questions
How do you calculate ROI?
ROI = (Final value − Cost) ÷ Cost × 100. For example, a $2,000 investment that grows to $2,500 has a gain of $500, for an ROI of 25%.
Should a discount be applied before or after tax on an invoice?
Before. Standard invoicing practice applies the discount to the subtotal first, then calculates tax on the discounted amount — not the original subtotal. Applying tax first and discounting afterward produces a different, generally incorrect total.
How do you add sales tax to a price?
Multiply the price by the tax rate (as a decimal) to get the tax amount, then add that to the original price. For example, $80 at 7% tax adds $5.60, for a total of $85.60.
How do you find the pre-tax price from a total that already includes tax?
Divide the total by (1 + tax rate as a decimal). For example, an $85.60 total that includes 7% tax has a pre-tax price of $85.60 ÷ 1.07 = $80.00 — simply subtracting 7% from the total gives an incorrect answer.