The half people get wrong by hand is the inclusive one. Removing 18% from a tax-inclusive figure is not the same as taking 18% off it, and the difference on a lakh is not small.
You have the taxable value and want the total. Multiply by the rate and add. A value of ₹10,000 at 18% gives ₹1,800 of tax and ₹11,800 to collect.
You have a figure that already contains the tax and want to know the taxable value. Divide by one plus the rate, not by the rate. ₹11,800 inclusive of 18% is ₹10,000 taxable and ₹1,800 tax — taking 18% off ₹11,800 gives ₹9,676, which is wrong by ₹324.
For a supply within the same state the tax splits equally into CGST and SGST — 18% becomes 9% plus 9%. For an inter-state supply the whole amount is IGST. The total is identical; which government receives it is not.
Divide by one plus the rate. At 18%, divide the inclusive figure by 1.18 to get the taxable value; the difference is the tax. Subtracting 18% from the inclusive figure gives a different and incorrect answer.
Equally. An 18% intra-state supply carries 9% CGST and 9% SGST. An inter-state supply carries the full 18% as IGST instead.
It follows the HSN classification, and the notified rates change. Our HSN finder can point you at the chapter, but confirm against the current rate notification for anything material.
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tBiz applies the rate, the split and the rounding on every invoice line.