UPDATE: I found [this webpage from Shika Law](https://www.shikalaw.com/post/japan-estate-tax-consideration-part-2-calculation-of-inheritance-tax-in-japan) that explains the calculation in English such that I am now able to understand the method in the tax law. The key to this webpage is that they very carefully define the terms they are using which helps avoid the confusion I had when reading the online translation of the other website I was originally using.
I was able to determine that the method in the tax law would result in the following equation (refer to diagram).
A = B – max( ( C – D ), 0), where D is the credit and D = ( E \* ( F / J ), where F = min ( ( G, 160M ), where G = (spouse’s actual share in %) \* ( J )
This equation is complicated, but only to the same extent that the method in the tax law is complicated. I’m sure the regulators have their reasons for doing it this way, but the equation can be simplified to an equivalent but more understandable method below.
Spouse’s credit = (share in %) \* ( Combined tax due prior to credits ), where the “share in %” is the spouse’s actual share but with a minimum and a cap. The minimum is the share in % if the spouse’s actual share was 160M. The cap is the spouse’s statutory share in %.
In hindsight, this is what the statement in the MOF diagram is saying about the credit, just not clearly (in my opinion anyway). Also, this is what was confirmed to me in the comments.
​
ORIGINAL POST:
TLDR: I’m looking for some “expert” help to understand the text of the inheritance tax law for calculating the spouse’s tax credit.
I’ve been trying to understand the calculation of spouse tax credit for inheritance tax. I’ve looked at a few websites with examples, and although they use similar methods, they are not completely consistent.
So this inspired me to read the text of the inheritance tax law, or at least the DeepL translation of it. The wording is pretty complicated, so I tried distilling it into some equations and marking up [this MOF diagram](https://www.mof.go.jp/english/policy/tax_policy/publication/tax011/e_all.pdf) (see below) accordingly.
I’m sure there are mistakes, due to misreading and/or bad translation. If you think you know what’s wrong, please explain in a comment.
**A = B – max( ( C – D ), 0 ), where D = E x ( F / E ), and where F = max( E, B )**
​
>DeepL Translation with my edits:
>
>Article 19-2 Where the spouse of a decedent has acquired property by inheritance or bequest from the decedent, the amount of inheritance tax payable by the spouse **\[A\]** shall be the amount of inheritance tax payable by the spouse **\[B\]**, if any, remaining after deducting the amount listed in item (ii) **\[D\]** from the amount listed in item (i) **\[C\]**. (2) Where the amount listed in item (i) is less than or equal to the amount listed in item (ii), there shall be no inheritance tax due and payable.
>
>(i) The amount calculated pursuant to the provisions of Articles 15 to 17 and the preceding Article with respect to the said spouse **\[C\]**
>
>(ii) The amount **\[D\]** calculated by multiplying the total amount of inheritance tax payable in respect of all persons who have acquired property as a result of the said inheritance or bequest **\[E\]** by the ratio of the lesser of the following amounts **\[F\]** to the total taxable amount of inheritance tax in respect of all persons who have acquired property as a result of the said inheritance or bequest **\[E\]**
>
>(a) The amount calculated by multiplying the total taxable amount of inheritance tax in respect of all persons who acquired property by inheritance or bequest by the spouse’s share of inheritance under Article 900 (Statutory Share of Inheritance) of the Civil Code (in the case of waiver of inheritance, the share of inheritance as if such waiver had not occurred) (in the case of the heir of the decedent in question (or the heir of the decedent in question (if there has been a waiver of inheritance, the share of inheritance as if there had been no waiver)) **\[E\]**
>
>(b) The amount equivalent to the taxable amount of inheritance tax in respect of the spouse who acquired the property by such inheritance or bequest. **\[B\]**
​
https://preview.redd.it/jzvcd0qwrojc1.png?width=1220&format=png&auto=webp&s=53163d203c772e0cac193b0d4af0f7c41355a501
For reference, here is the Japanese text of the inheritance tax law.
​
>第十九条の二 被相続人の配偶者が当該被相続人からの相続又は遺贈により財産を取得した場合には、当該配偶者については、第一号に掲げる金額から第二号に掲げる金額を控除した残額があるときは、当該残額をもつてその納付すべき相続税額とし、第一号に掲げる金額が第二号に掲げる金額以下であるときは、その納付すべき相続税額は、ないものとする。
>
>一 当該配偶者につき第十五条から第十七条まで及び前条の規定により算出した金額
>
>二 当該相続又は遺贈により財産を取得した全ての者に係る相続税の総額に、次に掲げる金額のうちいずれか少ない金額が当該相続又は遺贈により財産を取得した全ての者に係る相続税の課税価格の合計額のうちに占める割合を乗じて算出した金額
>
>イ 当該相続又は遺贈により財産を取得した全ての者に係る相続税の課税価格の合計額に民法第九百条（法定相続分）の規定による当該配偶者の相続分（相続の放棄があつた場合には、その放棄がなかつたものとした場合における相続分）を乗じて算出した金額（当該被相続人の相続人（相続の放棄があつた場合には、その放棄がなかつたものとした場合における相続人）が当該配偶者のみである場合には、当該合計額）に相当する金額（当該金額が一億六千万円に満たない場合には、一億六千万円）
>
>ロ 当該相続又は遺贈により財産を取得した配偶者に係る相続税の課税価格に相当する金額
​
by shrubbery_herring