We can give a derivation of an approximate main sequence lifetime formula making use of some assumed results:

First, the hydrogen burning rate (i.e., rate of burning to helium-4 (He-4)) is easily found.
We know the atomic masses of hydrogen (H, Z=1) and helium-4 (He-4, Z=2): respectively, 1.008 (fiducial value) and 4.002602 in atomic mass units (AMU).
When 4 hydrogen nuclei are hydrogen burned to 1 helium-4 (He-4), there is a relative atomic mass loss from reactants to product of 0.007291 = 0.7291 % ≅ 0.7 %.

Recall conservation of energy principle. So the rest mass is lost by the reactants is converted into some other form of energy. In fact, it is converted heat energy which can be calculated using E=mc**2.

Note

 E = mc**2, and thus 1 kilogram of rest mass in energy terms is

   1 kg * (3*10**8 m/s)**2 = 9*10**16 joules

   = about 2.5*10**10 KW-hours  (Note 1 kW-hr = 3.6*10**6 J )

   = the explosion energy yield of about 20 megatons of TNT
        ( 1 megaton TNT = about 4*10**15 J )  .

Now let's find the hydrogen burning rate in fiducial values:

  R = (rate of rest mass converted to heat energy)*[(H mass burnt)/(H mass converted)]

    = (L/c**2)*κ ,  where κ = [(H mass burnt)/(H mass converted)] = (1/0.007291)

    = (L_☉/c**2)*(L/L_☉)(1 M_☉ / 1.98855*10**30 kg)*(3.1557600*10**16 s / 1 Gyr)*κ

    = 9.270*10**(-3)*(L/L_☉)*(M_☉/Gyr)  .

We now assume the approximate mass-luminosity relation known from a combination of observations and stellar structure modeling: L = L_☉*(M/M_☉)**3.5 which holds approximately for the stellar mass 0.1--50 M_☉ (see Wikipedia: Main sequence: Lifetime, Wikipedia: Mass-luminosity relation). This gives us

  R = 9.270*10**(-3)*[(M/M_☉)**3.5]*(M_☉/Gyr)  .

Next, assuming luminosity is constant on the main sequence (which is approximately true), the main sequence lifetime formula is
```
  t_lifetime = fM/R = (10 Gyr)*(f/f_☉)*[(M_☉/M)**2.5] 
```
in general where we have rounded the coefficient from 10.78 to 10 since the 0.78 quantity is insignificant to the accuracy we are working at. Note f is the general hydrogen burning efficiency factor and f_☉ = 0.1 is a fiducial value for the Sun NOT an exact value. Thus,
```
  t_lifetime = fM/R = (10 Gyr)*(f/f_☉)*[(M/M_☉)**(-2.5)] in general  ,

                    = 10 Gyr for the Sun  ,

                    ≅ 3000 Gyr for a 0.1 M_☉ star assuming f ≅ 0.1  ,

                    ≅ 3*10**(-2) Gyr = 30 Myr for a 10 M_☉ star assuming f ≅ 0.1  . 
```
Note the hydrogen burning rate is for the hydrogen mass burnt. The rate of rest mass converted to heat energy is smaller by a factor of the relative atomic mass loss 0.007291.
Also note that if an initially pure hydrogen star converted all its hydrogen to helium-4 (He-4), it would decrease in mass by the same factor 0.007291.
Since the main-sequence lifetime of a star is overwhelmingly its longest phase as a nuclear burning object, our approximate main sequence lifetime formula applies to the whole nuclear burning lifetime of stars as well as the main-sequence lifetime.

Using our main sequence lifetime formula, we have calculated the values in Table: Approximate Main-Sequence Lifetimes.

  ____________________________________________________________________________
  Table:  Approximate Main-Sequence Lifetimes
  ____________________________________________________________________________
      M                       t
    (M_☉)                (Gyr or Myr)
  ____________________________________________________________________________
      0.1                 3,200 Gyr
      0.5                    57 Gyr
      0.88                   13.8 Gyr ≅ Gyr the age of the observable universe
      0.9                    13 Gyr
      1.0                    10 Gyr ≅ lifetime of a G2 V star (e.g., the Sun)
      1.5                     3.6 Gyr
      3                     640 Myr
      5                     180 Myr
      8                      55 Myr
     10                      32 Myr
     20                       5.6 Myr
     30                       2.0 Myr
     60                       0.36 Myr
  ____________________________________________________________________________

Our approximate stellar lifetimes in the above Table: Approximate Main-Sequence Lifetimes are NOT so bad as we can see by comparison to the more accurate results given in the image. However, NOT surprisingly our results become poorer as stellar mass increases well above 1 solar mass. They are also expected to be poorer as stellar mass decreases well below 1 solar mass, but the accurate results in the image do NOT give values for comparison in this case.