deliveréd the opinion of the Court.

The. respondent corporation manufactures lumber for shipment in interstate commerce, employing various men to pick up and stack boards. Prior to the trial in this case these stackers were compensated at agreed piece rates per thousand board feet ricked or stacked. The Administrator of the Wage and Hour Division of the Department of Labor brought suit to enjoin alleged violations of the overtime and record-keeping provisions of the Fair Labor Standards Act of 1938 1 in connection with these stackers. On the day before the commencement of the trial in the District Court the respondent ceased to use the allegedly illegal mode of piece rate compensation and entered into new and more elaborate wage agreements with the stack-ers. Following the trial the District Court dismissed the complaint and the Fifth Circuit Court of Appeals affirmed the judgment. 145 F. 2d 349. We granted certiorari because of important questions as to whether the new wage agreements comply with the requirements of § 7 (a) of the Act.

First. The District Court found that even though the former piece rate agreements be considered unlawful the respondent had no apparent intention of resuming their use. It also found no willful intention on the part of the respondent to violate the Act and no evidence of any intention of future violations. It therefore felt that there was no necessity for an injunction. While “voluntary discontinuance of an alleged illegal activity does not operate to remove a case from the ambit of judicial power,” Walling v. Helmerich & Payne, 323 U. S. 37, 43, it may justify a court’s refusal to enjoin future activity of this nature when it is combined with a bona fide intention to comply with the law and not to resume the wrongful acts. Cf. United States v. United States Steel Corp., 251 U. S. 417, 445. We cannot say, therefore, that the District Court abused its discretion in refusing to enjoin the abandoned method of wage payments.

At the same time, however, the validity of the new wage agreements was also at stake. These agreements on their face contemplated future hourly payments at regular and overtime rates as well as additional piece rate payments. Since the Administrator’s complaint alleged generally that the respondent was violating §§ 7 and 15 (a) (2) by employing its stackers on a piece work basis for more than 40 hours a week without compensating them for overtime at one and one-half times the regular rate, the question as to whether the new contracts satisfied § 7 (a) was properly in issue. Upon proof that these new provisions did not comply with § 7 (a) the Administrator was therefore entitled to an injunction absent any recognized mitigating factor. Evidence on this matter was introduced at the trial and the two courts below considered the contracts thoroughly, predicating their judgments in part upon the belief that the agreements did comply with § 7 (a). We accordingly turn to a consideration of that question.

Second. For approximately six months immediately preceding the trial the stackers were paid piece rates of 60 cents per thousand board feet ricked and 70 cents per thousand board feet stacked. During this period they earned at these rates an average of 51 cents an hour. Under the new contracts made on the day before the trial, however, they were compensated according to the following provisions:

“The basic or regular rate of pay is 35 cents per hour for the first forty hours each week and for time over forty hours each week the pay shall not be less than one and one-half times such basic or regular rate above mentioned with a guaranty that the employee shall receive weekly for regular time and for such overtime as the employee may work a sum arrived at as follows:

“The amount of stacking done by said employee shall be figured on the basis of 80 cents per thousand board feet of lumber for flat stacking and 70 cents per thousand board feet of lumber ricked.”

Using by way of illustration the labor performed and the hours worked during the six-month period preceding the trial, the Administrator points out that under the new guaranteed piece rates of 70 and 80 cents per thousand the stackers would earn an average of about 59 cents an hour for all hours actually worked, including those in excess of the statutory maximum. On the basis of the contract “regular rate” of 35 cents an hour, 2 on the other hand, the excess hours would yield the stackers only 52% cents hourly. It is thus apparent that the guaranteed piece rates would yield greater returns on an hourly basis for both regular and overtime work and that they would actually be the rates paid.

The respondent argues that these contract provisions satisfy § 7 (a) since they provide for a “regular rate” of 35 cents an hour and for payment of one and one-half times that rate, or 52% cents, for all overtime hours. Inasmuch as the Act does not forbid incentive pay or compensation above and beyond the statutory requirements it is urged that the additional payments resulting from the operation of the guaranteed piece rates are unaffected in any way by § 7 (a). We cannot agree, however, that this scheme of compensation is obedient to this statutory mandate.

Under § 7 (a) an employer is required to compensate his employees for all hours in excess of 40 at not less than one and one-half times the regular rate at which they are employed. Thus by increasing the employer’s labor costs by 50% at the end of the 40-hour week and by giving the employees a 50% premium for all excess hours, § 7 (a) achieves its dual purpose of inducing the employer to reduce the hours of work and to employ more men and of compensating the employees for the burden of a long workweek. Overnight Motor Co. v. Missel, 316 U. S. 572, 577-578; Walling v. Helmerich & Payne, supra, 40; Jewell Ridge Coal Corp. v. Local No. 6167, ante, pp. 161, 167.

The keystone of § 7 (a) is the regular rate of compensation. On that depends the amount of overtime payments which are necessary to effectuate the statutory purposes. The proper determination of that rate is therefore of prime importance.

As we have previously noted, the regular rate refers to the hourly rate actually paid the employee for the normal, non-overtime workweek for which he is employed. Walling v. Helmerich & Payne, supra, 40; United States v. Rosenwasser, 323 U. S. 360, 363. In the case of piece work wages, this regular rate coincides with the hourly rate actually received for all hours worked during the particular workweek, such rate being the quotient of the amount received during the week divided by the number of hours worked. See Overnight Motor Co. v. Missel, supra, 580. As long as the minimum hourly rates established by § 6 are respected, the employer and employee are free to establish this regular rate at any point and in any manner they see fit. They may agree to pay compensation according to any time or work measurement they desire. United States v. Rosenwasser, supra. “But this freedom of contract does not include the right to compute the regular rate in a wholly unrealistic and artificial manner so as to negate the statutory purposes.” Walling v. Helmerich & Payne, supra, 42. The regular rate by its very nature must reflect all payments which the parties have agreed shall be received regularly during the workweek, exclusive of overtime payments. It is not an arbitrary label chosen by the parties; it is an actual fact. Once the parties have decided upon the amount of wages and the mode of payment the determination of the regular rate becomes a matter of mathematical computation, the result of which is unaffected by any designation of a contrary “regular rate” in the wage contracts.

Here it is established that under the new wage agreements the stackers will receive 70 or 80 cents per thousand board feet ricked or stacked. Translated to an hourly basis this means that they will receive approximately 59 cents per hour for both regular and overtime hours. 3 That amount is guaranteed them under the terms of the contracts and accurately mirrors all payments that they normally will receive from the respondent during the workweek. This 59-cent figure is therefore the average regular rate at which the stackers are employed. The individual regular rate which must be used depends, of course, upon the number of hours worked and the wages received by each stacker during the particular workweek in question. But such a rate is the one that must enter into any calculations of overtime payments due under §7 (a). Insofar as the wage agreements failed to provide for the payment of one and one-half times this regular rate for all overtime hours, they plainly violated the requirements of § 7 (a).

The 35-cent per hour “regular rate” fixed by the contracts is obviously an artificial one, however bona fide it may have been in origin. Except in the extremely unlikely situation of the piece work wages falling below a 35-cent per hour figure, this “regular rate” is never actually paid. In the normal case where the stackers earn more than 35 cents per hour on the piece rate basis during non-overtime hours, they are guaranteed this higher figure and are actually so compensated. And even when the stackers work overtime they actually receive at the present time an average of 69 cents an hour under the guaranteed piece rate system rather than one and one-half times the 35-cent “regular rate.”

The 35-cent figure thus does not constitute the hourly rate actually paid for the normal, non-overtime workweek. Nor is it used as the basis for calculating the compensation received for overtime labor. It is not in fact the regular rate under any normal circumstances. And reliance upon it to prove compliance with § 7 (a) only allows respondent to escape completely the burden of a 50% premium for the hours so worked and prevents the stackers from receiving the benefits of such a premium as Congress intended. Thus by a mere label respondent would be enabled to nullify all the purposes for which § 7 (a) was created. We are unable to perceive any reason for sanctioning that result.

This Court’s decision in Walling v. Belo Corp., 316 U. S. 624, lends no support to respondent’s position. The particular wage agreements there involved were upheld because it was felt that in fixing a rate of 67 cents an hour the contracts did in fact set the actual regular rate at which the workers were employed. The case is no authority, however, for the proposition that the regular rate may be fixed by contract at a point completely unrelated to the payments actually and normally received each week by the employees.

The judgment of the court below is reversed with directions to remand the case to the District Court for further proceedings consistent with this opinion.

Reversed.