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Stock-based Compensation (Narrative) (Details) - USD ($) | 12 Months Ended
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Aug. 31, 2022 | Aug. 31, 2021 | Aug. 31, 2020
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Number of shares authorized under stock plan |  | 1,000,000 |  |
Number of shares available for grant |  | 384,859 |  |
Allocated share-based compensation expense |  | $ 6,697,000 | $ 9,555,000 | $ 5,358,000
Employee service share-based, Tax benefit from compensation expense |  | $ 1,500,000 | 2,000,000.0 | 1,200,000
Restricted Stock Units [Member] |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Granted, Number of Shares |  | 23,461 |  |
Allocated share-based compensation expense |  | $ 4,153,000 | 3,656,000 | 3,325,000
Employee service share-based, Tax benefit from compensation expense |  | 600,000 | $ 1,900,000 | $ 1,200,000
Compensation cost not yet recognized |  | $ 1,400,000 |  |
Remaining weighted-average vesting periods |  | 1 year 5 months 12 days |  |
Weighted-average grant date fair value |  | $ 217.03 | $ 208.29 | $ 184.43
Total intrinsic value of stock-based awards converted into common shares |  | $ 3,000,000.0 | $ 8,500,000 | $ 5,400,000
Market Share Units [Member] |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Granted, Number of Shares |  | 13,195 |  |
Allocated share-based compensation expense |  | $ 2,544,000 | 2,294,000 | 2,033,000
Employee service share-based, Tax benefit from compensation expense |  | 900,000 | $ 1,300,000 | $ 900,000
Compensation cost not yet recognized |  | $ 3,100,000 |  |
Remaining weighted-average vesting periods |  | 1 year 9 months 25 days |  |
Weighted-average grant date fair value |  | $ 232.99 | $ 184.96 | $ 216.77
Total intrinsic value of stock-based awards converted into common shares |  | $ 4,400,000 | $ 5,900,000 | $ 4,400,000
Expected volatility period |  | 2 years 10 months 20 days | 2 years 10 months 17 days | 2 years 10 months 24 days
Percent of original target number of vested shares |  | 100.00% |  |
Expected dividend yield |  | 0.00% | 0.00% | 0.00%
Deferred Performance Units [Member] |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Granted, Number of Shares |  |  | 0 |
Compensation cost not yet recognized |  | $ 0 |  |
Performance Share Units [Member] |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Granted, Number of Shares |  | 18,684 |  |
Allocated share-based compensation expense | [1] |  | $ 3,605,000 |
Employee service share-based, Tax benefit from compensation expense |  | $ 800,000 | $ 0 | $ 0
Compensation cost not yet recognized |  | $ 0 |  |
Weighted-average grant date fair value |  | $ 227.24 | $ 197.51 |
Total intrinsic value of stock-based awards converted into common shares |  | $ 4,000,000.0 |  |
Vesting percentage |  |  | 100.00% |
Key Executives [Member] | Restricted Stock Units [Member] |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Vesting period |  | 3 years |  |
High Level Employees [Member] | Restricted Stock Units [Member] |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Vesting period |  | 3 years |  |
High Level Employees [Member] | Market Share Units [Member] |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Vesting period |  | 3 years |  |
Minimum [Member] | Performance Share Units [Member] |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Vesting percentage |  | 0.00% |  |
Maximum [Member] | Market Share Units [Member] |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Percent of original target number of vested shares |  | 200.00% |  |
Maximum [Member] | Performance Share Units [Member] |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Vesting percentage |  | 100.00% |  |
[1] | PSU awards, similar to DPU awards that were replaced by PSUs in fiscal year 2021, contain performance conditions for which accrual of expense is based on the probable outcome of the performance conditions. Vesting of DPUs related to the measurement year of 2020 was deemed not probable at the end of the fiscal year. DPUs were then discontinued by the Company beginning in fiscal year 2021. PSUs pertaining to the measurement year of fiscal year 2021 vested at 100% since the performance conditions were fully achieved. PSUs pertaining to the measurement year of fiscal year 2022 was deemed not probable at the end of the fiscal year.

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- Definition Amount of expense for award under share-based payment arrangement. Excludes amount capitalized. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (h)(1)(i) -URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901 + Details
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- Definition Weighted-average period over which cost not yet recognized is expected to be recognized for award under share-based payment arrangement, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (i) -URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901 + Details
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- Definition Amount of tax benefit for recognition of expense of award under share-based payment arrangement. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (h)(1)(i) -URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901 + Details
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- Definition Period over which grantee's right to exercise award under share-based payment arrangement is no longer contingent on satisfaction of service or performance condition, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days. Includes, but is not limited to, combination of market, performance or service condition. + References Reference 1: http://www.xbrl.org/2003/role/exampleRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (a)(1) -URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901 + Details
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- Definition The number of grants made during the period on other than stock (or unit) option plans (for example, phantom stock or unit plan, stock or unit appreciation rights plan, performance target plan). + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (c)(2)(iii)(01) -URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901 + Details
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- Definition The weighted average fair value at grant date for nonvested equity-based awards issued during the period on other than stock (or unit) option plans (for example, phantom stock or unit plan, stock or unit appreciation rights plan, performance target plan). + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (c)(2)(iii)(01) -URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901 + Details
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- Definition The estimated dividend rate (a percentage of the share price) to be paid (expected dividends) to holders of the underlying shares over the option's term. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (f)(2)(iii) -URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901 + Details
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- Definition The difference between the maximum number of shares (or other type of equity) authorized for issuance under the plan (including the effects of amendments and adjustments), and the sum of: 1) the number of shares (or other type of equity) already issued upon exercise of options or other equity-based awards under the plan; and 2) shares (or other type of equity) reserved for issuance on granting of outstanding awards, net of cancellations and forfeitures, if applicable. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901 + Details
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