according to equation vs based on equation

Both 'according to equation' and 'based on equation' are correct phrases, but they are used in slightly different contexts. 'According to equation' is commonly used when referring to a specific equation or formula, while 'based on equation' is more often used to indicate that something is derived or determined from an equation.

Last updated: March 26, 2024 • 2590 views

This phrase is correct and commonly used when referring to a specific equation or formula.

"according to equation"

This phrase is used to introduce information that is derived from a particular equation or formula.

Examples:

According to equation 2, the velocity of the object is directly proportional to the force applied.
The temperature can be calculated according to equation 5 in the textbook.

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The particulate mass shall be calculated according to equation 27 of paragraph 8.3.
The capacity factors k' are calculated from the dead time to and retention times tR of the selected reference substances according to equation 4 (see Section 1.2).
The actual NO concentration shall be calculated at the gas divider's outlet, xNOact, based on the span gas concentrations and xCO2act according to equation (8-5).
actual concentration of NO when NO span gas is blended with CO2 span gas, according to sub-paragraph (k) of paragraph 8.1.11.1.4. and calculated according to equation (8-5)
is the fuel specific factor according to equation 11 in paragraph 8.1.1.
The WHTC hot start emissions shall be weighted according to equation 5 where e-
One set shall be calculated using uncorrected concentrations and another set shall be calculated using the concentrations corrected for drift according to equation 66.
Images per Job: Except for fax machines, the number of images shall be computed according to Equation 9, below.
The calibration factor, Φa by which all the instrument readings must be multiplied, shall be determined according to equation (1).
The mean of the series of DRc values is calculated and in addition the standard deviation according to equation [4]
The arithmetic mean values over the 30 s period shall be used to calculate the least squares linear regression parameters according to equation 6 in paragraph 7.7.2.
The calibration factor, Öa by which all the instrument readings must be multiplied, shall be detemined according to equation (1):

Alternatives:

as per the equation
in accordance with the equation
following the equation
in line with the equation
per the equation

This phrase is correct and commonly used to indicate that something is derived or determined from an equation.

"based on equation"

This phrase is used to show that a conclusion, decision, or action is made after considering or deriving information from an equation.

Examples:

The new model was developed based on equations derived from quantum mechanics.
The prediction was made based on the equation provided by the researcher.

Show examples from the web [+]

The contribution formula is based on the equation:
Based on the basic equations of motion:
Subsequent infusion rates should be calculated based on the actual FVIII levels and recalculated clearance for each day post surgery based on the equation: clearance = infusion rate/ actual FVIII level.
She came up with this equation based on global tidal patterns, and-and-and... she was fixated on this certain sequence of numbers, and I... I know she was trying to tell us something.
Calibration of the CFV is based upon the flow equation for a critical venturi.
How does the Council intend to turn the purely accountancy-based equation into a genuine political success, by putting fresh funding into PDA commitments instead of hiding behind the Stability Pact to justify nothing more than additional moratoria?
Calibration of the SSV is based upon the flow equation for a subsonic venturi.
Calibration of the CFV is based upon the flow equation for a critical venturi:
This equation is based upon the carbon balance assumption (carbon atoms supplied to the engine are emitted as CO
This equation is based upon the carbon balance assumption (carbon atoms supplied to the engine are emitted as CO2) and determined through the following steps:
This equation is based upon the carbon balance assumption (carbon atoms supplied to the engine are emitted as CO2) and derived through the following steps:
Equations for calculating the flight profile from the required propulsion and aerodynamic parameters are given in Appendix B. Each equation contains coefficients (and/or constants) which are based on empirical data for each specific aircraft type.
5.1.2 Health safety is not the result of some equation or formula; it is based on the spirit of precaution and contradiction.
The limit of detection for immunoassays is determined as 3 x the standard deviation, based on 10 replicate analysis of the blank, to be divided by the slope value of the linear regression equation.
The actual NO concentration shall be calculated at the gas divider's outlet, xNOact, based on the span gas concentrations and xCO2act according to equation (8-5).
The change of the substance concentration in the solution determines the statistical accuracy of the measurement based on the form of adsorption equation and the limit of the analytical methodology, in detecting the concentration of the chemical in solution.
The limit of detection for immunoassays is determined as the sum of the mean and 3x the standard deviation, based on 10 replicate analysis of the blank, to be divided by the slope value of the linear regression equation.
Based on currently available information, the programme appears to be based on plausible growth assumptions.
But despite the obvious problems with Nash's theories, the young technocrats at RAND were convinced that in them lay the seeds of a new form of ordering society, based on the free individual, because the equations provided a scientific basis
equation: an expression used to represent a concept based on a statement that two mathematical expressions are, for instance, equal as identified by the equal sign (=), or assigned to one another by a similar sign

Alternatives:

derived from the equation
determined by the equation
concluded from the equation
inferred from the equation
following the equation

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according to equation vs based on equation