delivered the opinion of the Court.

The commissioner determined ,a deficiency of $9,156.69 on account of respondent’s 1928 income tax. The Board of Tax Appeals made the same determination. The court held it excessive and that the evidence did not show the correct amount, reversed the order of the board, and remanded the case for further proceedings in accordance with the opinion. 70 F. (2d) 619. The petition for our writ states the question: “ Whether the Circuit Court of Appeals erred in remanding this case to the Board of Tax Appeals for a new hearing on the ground that the Commissioner’s determination of the amount of income was incorrect, although the taxpayer had failed to prove facts from which a correct determination could be made.”

In August, 1927, respondent acquired all the stock of four utilities at a total cost of $96,030, organized a holding company and, October 13, transferred to it all the *509utilities stock and received therefor all the shares of the holding company: 1,000 of preferred having no par value, entitled to a dividend of $6 annually, $100 on liquidation and callable ,at $105 per share; 2,500 of no par value class A common callable at $35 per share; 5,000 of no p'ar value class B common stock having the voting power. As this transaction was “ reorganization ” under Revenue Act of 1926, § 203 (b) (2), 44 Stat. 12, no taxable gain resulted.

In May, 1928, the holding company sold the stock of the four utilities to the Colonial corporation for $194,-930.16. Later in that year the holding company bought or retired all the preferred and paid the taxpayer $99,000 therefor. In his 1928 return he assigned the $96,030 for which he procured the utilities to the preferred stock of the holding company, deducted that amount from the $99,000 received therefor, and reported the difference, $2,970, as the gain derived from the sale. The applicable statutory provisions are contained in Revenue Act of 1928. §§ 111 (a) (d), 112 (b) (3), 113 (a) (6). 45 Stat. 815-19.1 *510They prescribe no rule that is applicable for the ascertainment of the cost of the preferred stock or the apportionment of the total cost between preferred and common. But Regulations 74, Art. 58, declares: “Where common stock is received as a bonus with the purchase of preferred stock or bonds, the total purchase price shall be fairly apportioned between such common stock and the securities purchased for the purpose of determining the portion of the cost attributable to each class of stock or securities, but if that should be impracticable in any case, no profit on any subsequent sale of any part of the stock or securities will be realized until out of the proceeds of sales shall have been recovered the total cost.”

The Commissioner, holding the taxpayer not entitled to charge the cost of all to the preferred, apportioned between the preferred and common. He made his calculation upon the assumption that the cost, in 1927, attributable to the preferred shares bears the same relation to cost of all the shares then acquired as the amount respondent received, in 1928, for the preferred bears to the amount paid the holding company by Colonial corporation for all the utilities shares.2 On that basis, he found that of the total 1927 cost, $96,030, there was chargeable to the preferred only $48,771.16 which deducted from $99,000 received by respondent for the preferred in 1928, leaves $50,228.84 upon which he determined the deficiency of $9,156.69.

*511Before the Board of Tax Appeals the taxpayer introduced evidence to show the details of the transaction and that there was no change in value of the utilities stock between the time he got it in August, 1927, and the date, October 13 of the same year, on which he transferred it to the holding company in exchange for its shares and that the entire increase in value came after that transfer. No opposing evidence was offered. On the facts shown, the taxpayer maintained that, as total cost was less than $100 per share for the preferred having prior rights to that extent on liquidation, the common stock had no value. Rejecting that contention, the Board of Tax Appeals filed a memorandum opinion in which it said: “ It may well be that the properties acquired or all the classes of stocks received by the petitioner were worth only $96,030 . . .. and yet the preferred stock . . . may have had the value of $48,771.16 ... It is obvious that even if all the securities were worth only $96,030 that the proportionate value of the preferred stock to all the stocks would not necessarily be different from that determined by the Commissioner. . . . The question ... is one of fact to be determined by testimony and not theory. It is conceivable that common stocks may actually sell on the market when preferred stocks in the same corporation are selling at less than par.” It was upon that basis, without specific findings of fact, that the board made the redetermination at the figure set by the commissioner.

The only question for consideration is that stated in the petition for the writ of certiorari. Gunning v. Cooley, 281 U. S. 90, 98. That question in effect assumes, and here it is taken as granted, that the court rightly held the evidence sufficient to require a finding that the commissioner’s apportionment of total cost as between preferred and common stock was unfair and erroneous and that therefore the commissioner’s determination was exces*512sive. We also assume that the total purchase price is susceptible of fair apportionment and that upon another hearing the correct amount may be found. 70 F. (2d) 619, 620. Regulations 74, Art. 58, supra. The point to be considered is whether, the taxpayer having failed to establish the correct amount to be assigned to the preferred stock as its cost to him, the court erred in reversing and remanding for further proceedings in accordance with its opinion.

The commissioner does not contend that, in cases where Circuit Courts of Appeals properly reverse determinations of the board, they are without power to remand for further hearing in the nature of a new trial.3 His contention is that in this case the burden on the taxpayer was not only to prove that the commissioner’s determination is erroneous but to show the correct amount of the tax. In substance he says that, because of the taxpayer’s failure to establish facts on which a fair apportionment may be made, the board’s redetermination at the commissioner’s erroneous figure was valid, and there being no error of law, should have been sustained by the court. And he maintains that, in the absence of error on the part of the board, the court was without power to remand for further hearing.

He cites Revenue Act of 1926, § 274 (e), 44 Stat. 56: “ The Board shall have jurisdiction to redetermine the correct amount of the deficiency even if the amount so redetermined is greater than the amount of the deficiency, *513notice of which has been mailed to the taxpayer, and to determine whether any penalty, additional amount or addition to the tax should be assessed, if claim therefor is asserted by the Commissioner at or before the hearing or a rehearing.” The purpose of that provision is to define the jurisdiction granted to the board; it does not prescribe any rule of evidence or burden of proof. Plainly it does not support the commissioner’s contention that the taxpayer, even though he has shown the determination to be arbitrary and excessive, must nevertheless pay the added tax because he has not also shown that he owes nothing or the correct amount, if any, that legally may be laid upon him.

He also cites Revenue Act of 1928, §§51 (a) and 54 (a). 45 Stat. 807, 808. Neither gives any support to his contention. The first requires the taxpayer to make under oath a return stating specifically the amount of his gross income and the amounts of deductions and credits allowed. The other requires the taxpayer to keep such records, render under oath such statements, make such returns, and comply with such rules and regulations as the commissioner may prescribe. These requirements give no support to the commissioner’s contention. They tend rather to suggest that taxpayer’s returns are correct and may not arbitrarily be set at naught.

He also cites Rule 30 adopted by the board: “ The burden of proof shall be upon the petitioner, except as otherwise provided by statute and except that in respect of any new matter pleaded in his answer, it shall be upon the respondent.” But there is nothing in it to suggest intention to require the taxpayer to prove not only that a deficiency assessment laid upon him was arbitrary and wrong but also to show the correct amount. Moreover, the board held the evidence not sufficient to show the *514apportionment erroneous and on that ground alone sustained' the assessment. Necessarily the board did not come to the question that is here presented as to burden of proof. The fact that the commissioner’s determination of a deficiency was arbitrarily made may reasonably be deemed sufficient to require the board to set it aside. Cf. Bruce & Human Drug Co., 1 B. T. A. 342. Acorn Refining Co., 2 B. T. A. 253. Index Notion Co., 3 B. T. A. 90.

The commissioner cites United States v. Rindskopf, 105 U. S. 418; United, States v. Anderson, 269 U. S. 422, 443; Reinecke v. Spalding, 280 U. S. 227, 232-233. The first of these may be put aside without discussion as having no bearing upon the point here in controversy.. The other two were adequately distinguished by the Circuit Court of Appeals. Each was an action to recover taxes paid. Obviously the burden was on the plaintiff, in order to establish a basis for judgment in his favor, specifically to show not merely that the assessment was erroneous but also the amount to which he was entitled. For like reason the burden is upon the taxpayer to establish the amount of a deduction claimed. Burnet v. Houston, 283 U. S. 223, 227. Helvering v. Independent Life Ins. Co., 292 U. S. 371, 381. New Colonial Co. v. Helvering, 292 U. S. 435, 440.

We find nothing in the statutes, the rules of the board or our decisions that gives any support to the idea that the commissioner’s determination, shown to be without rational foundation and excessive, will be enforced unless the taxpayer proves he owes nothing or, if liable at all, shows the correct amount. While decisions of the lower courts may not be harmonious, our attention has not *515been called to any that persuasively supports the rule for which the commissioner here contends.4

Unquestionably the burden of proof is on the taxpayer to show that the commissioner’s determination is invalid. Lucas v. Structural Steel Co., 281 U. S. 264, 271. Wickwire v. Reinecke, 275 U. S. 101, 105. Welch v. Helvering, 290 U. S. 111, 115. Frequently, if not quite generally, evidence adequate to overthrow the commissioner’s finding is also sufficient to show the correct amount, if any, that is due. See, e. g., Darcy v. Commissioner, 66 F. (2d) 581, 585. But, where as in this case the taxpayer’s evidence shows the commissioner’s determination to be arbitrary and excessive, it may not reasonably be held that he is bound to pay a tax that confessedly he does not owe, unless his evidence was sufficient also to establish the correct amount that lawfully might be charged against him. On the facts shown by the taxpayer in this case, the board should have held the apportionment arbitrary and the commissioner’s determination invalid. Then, upon *516appropriate application that further hearing be had, it should have heard evidence to show whether a fair apportionment might be made and, if so, the correct amount of the tax.- The rule for which the commissioner here contends is not consonant with the great remedial purposes of the legislation creating the Board of Tax Appeals.5 The Circuit Court of Appeals rightly reversed and remanded the case for further proceedings in accordance with its opinion.

Affirmed.

dissenting.

I think the judgment should be reversed.

As respondent failed to establish any amount by which the deficiency fixed by the Commissioner should be reduced, the Board of Tax Appeals was without authority, under the statute defining its jurisdiction, to disturb the determination of the Commissioner, c. 27, §§ 274 (b) (e), 906 (c) (d), 44 Stat. 9, 55, 56, 107; 26 U. S. C., §§ 1048a, 1048c, 1217 (c) (d). If, under § 906 (d), it was the duty of the Board to dismiss the petition and enter on its records ,a finding that it could not determine the amount of the deficiency, these requirements are formal only. Its failure to comply with them does not require a reversal of its order sustaining the action of the Commissioner or in any case afford ground for decision on appeal that the Board should have held the Commissioner’s determination invalid or that'it should now take further evidence.