Core answer: Tax-inclusive price ÷ (1 + tax rate) = tax-exclusive price; tax = inclusive price × rate ÷ (1 + rate). At 13% VAT: ¥113 inclusive = ¥100 net + ¥13 tax. Common mistake: computing tax as inclusive × 13% = ¥14.69 — wrong, because the tax base is the NET price, not the gross. Quick formulas: net = gross ÷ 1.13 (or 1.09 / 1.06 / 1.03 / 1.01 for other rates).
The formula set
- Net (不含税) = Gross ÷ (1 + rate)
- Tax = Gross − Net = Gross × rate ÷ (1 + rate)
- Gross (含税) = Net × (1 + rate)
| Rate | Net from ¥1,000 gross | Tax |
|---|---|---|
| 13% | ¥884.96 | ¥115.04 |
| 9% | ¥917.43 | ¥82.57 |
| 6% | ¥943.40 | ¥56.60 |
| 3% | ¥970.87 | ¥29.13 |
| 1% | ¥990.10 | ¥9.90 |
When you need it
- Accounting entries — books record net revenue and 应交税费 separately.
- Quoting prices — "¥10,000 含税" vs "¥10,000 不含税" differ by the full tax amount.
- Invoice checking — a 专用发票 shows net + tax lines; verify the math.
- Contract disputes — ambiguous "tax included" language causes real lawsuits; always write 含税/不含税 explicitly.
Worked examples
Example 1 — Quote comparison. Vendor A: ¥11,300 含税 13% (net ¥10,000). Vendor B: ¥10,600 不含税 → gross ¥11,978. A is ¥678 cheaper despite B's "lower" number — always compare on the same basis.
Example 2 — General taxpayer margin. Sell at ¥22,600 含税 (net ¥20,000, output tax ¥2,600); buy materials ¥11,300 含税 (net ¥10,000, input tax ¥1,300). VAT payable = 2,600 − 1,300 = ¥1,300. The split is how input credits are computed.
Example 3 — Reimbursement trap. Expensing a ¥565 普票 vs 专票 at 6%: the 专票 lets the company credit ¥31.98 of tax — same receipt, 5.7% cheaper for the company. Finance teams reject 普票 for exactly this reason.
Common mistakes and myths
- Tax = gross × rate — the #1 error; tax = gross × rate ÷ (1+rate). At 13% the difference is 1.5 percentage points of revenue.
- Mixing rates — goods 13%, transport 9%, modern services 6%; a combined invoice needs line-by-line rates, not one blended guess.
- Forgetting small-scale rules — 小规模纳税人 uses 3% (often reduced to 1%) levy WITHOUT input credits; their "含税" math uses the levy rate.
- Rounding drift — split per line then sum, not sum then split; invoice systems (航天信息/百旺) round each line to ¥0.01.
- Assuming all prices are gross — B2B quotes are often 不含税 by convention; confirm before wiring money.