Stockholders' equity - Weighted Average Assumptions (Details) - Tecogen - Stock Options	12 Months Ended
Dec. 31, 2022	Dec. 31, 2021
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Expected life	6 years 3 months	6 years 3 months
Risk-free interest rate	2.17%	1.09%
Expected volatility	36.24%	35.86%

The estimated measure of the percentage by which a share price is expected to fluctuate during a period. Volatility also may be defined as a probability-weighted measure of the dispersion of returns about the mean. The volatility of a share price is the standard deviation of the continuously compounded rates of return on the share over a specified period. That is the same as the standard deviation of the differences in the natural logarithms of the stock prices plus dividends, if any, over the period.

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- Definition

The risk-free interest rate assumption that is used in valuing an option on its own shares.

+ References

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- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

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- Definition

Expected term of award under share-based payment arrangement, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.

+ References

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