Mahtani ratio

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Mahtani ratio

The Mahtani ratio is a second-order growth metric used in financial and business analytics to measure the rate of change in growth across multiple time periods. It quantifies how the growth rate itself is accelerating or decelerating over time, based on at least three consecutive data points (such as quarterly revenue, profits, or user counts). The ratio is expressed as a percentage.

Definition

Given a sequence of at least three consecutive values:

$Q_0,Q_1,Q_2,...,Q_n$

Define first-order differences (growth deltas) as:

${\mathrm{\Delta }}_i=Q_{i+1}-Q_i$   for $i=0,1,...,n-1$

Then, the Mahtani ratio is computed as the average of the percentage change between consecutive deltas:

$\text{Mahtani ratio}=\frac{1}{n-2}\sum _{i=0}^{n-3}(\frac{{\mathrm{\Delta }}_{i+1}-{\mathrm{\Delta }}_i}{{\mathrm{\Delta }}_i}\times 100)$

Interpretation

• Positive values indicate accelerating growth.
• Zero indicates steady, linear growth.
• Negative values indicate decelerating growth or a slowdown.
• The metric accounts for both positive and negative growth, and does not use absolute values—making it sensitive to directional shifts in performance.

Minimum data requirement

The Mahtani ratio requires at least three consecutive data points, as it is based on comparing two growth deltas (i.e., two first-order changes).

Example

Consider a company’s quarterly revenue (in millions):

Quarter	Revenue
Q0	–1000
Q1	–100
Q2	100
Q3	500

Compute the growth deltas:

${\mathrm{\Delta }}_0=-100-(-1000)=900$

${\mathrm{\Delta }}_1=100-(-100)=200$

${\mathrm{\Delta }}_2=500-100=400$

Compute the Mahtani terms:

$R_0=\frac{200-900}{900}\times 100=-77.78\mathrm{\%}$

$R_1=\frac{400-200}{200}\times 100=100.00\mathrm{\%}$

Then the Mahtani ratio is:

$\text{Mahtani ratio}=\frac{-77.78+100}{2}=11.11\mathrm{\%}$

Applications

The Mahtani ratio is useful in:

• Startup growth analysis
• Revenue trend diagnostics
• KPI trajectory monitoring
• Investment comparisons, especially where traditional growth percentages are misleading due to sign changes

Comparison with traditional growth metrics

While standard growth metrics compare two values directly (e.g., $\frac{Q_2-Q_1}{Q_1}$), the Mahtani ratio examines the change in growth rate over time—offering a richer view of momentum, inflection points, and trend reversals.

For example:

• Going from –1000 → –100 → 100 shows strong momentum, but traditional percent change from –100 to 100 would misleadingly show a –200% growth.
• The Mahtani ratio, in contrast, reflects the acceleration in performance.

See also

• Sharpe ratio
• Growth rate
• Second derivative
• Compound annual growth rate

References

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