Academic Citation Impact (h-Index, m-Quotient, g-Index & Citation Velocity) Calculator

Analyze scholar citation impact via h-index, career-normalized m-quotient, and Lotka/Hirsch ratio a = Citations/h².

Hirsch Career-Normalized m-Quotient
1.8 h / year
Hirsch Proportionality Ratio (Citations / h²) 4.475 a ratio
Excess Citations Above h² Core 1,126 citations
Projected h-Index in 5 Years 24.334 h-index
Inputs
⚡ Scenarios:
h-index
Author’s current Hirsch h-index (h papers with at least h citations each).
citations
Total cumulative citations across all published papers.
years
Academic age in years since first peer-reviewed publication.
cit/yr
Current annual citation velocity (citations/year).
Results & Graph
Hirsch Career-Normalized m-Quotient
1.8 h / year
Hirsch Proportionality Ratio (Citations / h²)
4.475 a ratio
Excess Citations Above h² Core
1,126 citations
Projected h-Index in 5 Years
24.334 h-index

Hirsch Career-Normalized m-Quotient

Graph 1 • Academic h-Index & m-Quotient • Domain Architecture & Live Telemetry Maps Current H Index, Total Career Citations, Years Since First Publication through Academic h-Index & m-Quotient Formula.
Hirsch Career-Normalized m-Quo: 1.8 h / year Academic h-Index & m-Quotient • Invariants & Metrics Hirsch Career-Normalized m-Q 1.8 h / year Hirsch Proportionality Ratio 4.475 a ratio Excess Citations Above h² Co 1,126 citations Projected h-Index in 5 Years 24.334 h-index
Graph 2 • Hirsch Career-Normalized m-Quotient Across Current H Index Sweep (40% → 160%) Evaluates m_Quotient = h_Index / AcademicAgeYears; HirschProportionality_a = Tot across 7 operating points (current input highlighted).
0 h / ye 1.59 h / ye 3.19 h / ye 0.700 7.20 1.10 10.80 1.40 14.40 1.80 18 2.20 21.60 2.50 25.20 2.90 28.80
Graph 3 • Joint Sensitivity: Current H Index × Total Career Citations Compares Hirsch Career-Normalized m-Quotient when Total Career Citations is shifted +25% (solid) vs. −25% (dashed).
0 h / ye 1.26 h / ye 2.53 h / ye --- Total Career Citations @ 75% 1.30 -30% 1.50 -15% 1.80 +0% 2.10 +15% 2.30 +30%
Summary: An h-index of 18 over 10 years gives an m-quotient of 1.8 (Hirsch proportionality constant a = Citations/h² = 4.48) and projects to h ≈ 24.3 in 5 years.
Summary: An h-index of 18 over 10 years gives an m-quotient of 1.8 (Hirsch proportionality constant a = Citations/h² = 4.48) and projects to h ≈ 24.3 in 5 years.
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Formula & Mathematical Methodology: Academic h-Index & m-Quotient Formula

mQuotient = hIndex / AcademicAgeYears
HirschProportionalitya = TotalCitations / (hIndex)² (typically 3 ≤ a ≤ 5)
m_Quotient = h_Index / AcademicAgeYears; HirschProportionality_a = TotalCitations / (h_Index)² (typically 3 ≤ a ≤ 5)
  • currentHIndex: Author’s current Hirsch h-index (h papers with at least h citations each).
  • totalCareerCitations: Total cumulative citations across all published papers.
  • yearsSinceFirstPublication: Academic age in years since first peer-reviewed publication.
  • annualNewCitationsVelocity: Current annual citation velocity (citations/year).

Rounding: Internal floating-point calculations run in 64-bit IEEE-754 double precision; display values round to 2–4 decimal places.

Worked Example: Academic h-Index & m-Quotient Worked Example

Analyze scholar citation impact via h-index, career-normalized m-quotient, and Lotka/Hirsch ratio a = Citations/h².

  1. Enter the input measurement, system configuration, or astronomical parameter.
  2. Apply the standard conversion or analytical equation: m_Quotient = h_Index / AcademicAgeYears; HirschProportionality_a = TotalCitations / (h_Index)² (typically 3 ≤ a ≤ 5).
  3. Inspect the primary metric, secondary equivalents, and 3 real-time SVG graphs.
Result: Computes Academic h-Index & m-Quotient via m_Quotient = h_Index / AcademicAgeYears; HirschProportionality_a = TotalCitations / (h_Index)² (typically 3 ≤ a ≤ 5).

Frequently Asked Questions

How does the Academic Citation Impact (h-Index, m-Quotient, g-Index & Citation Velocity) Calculator perform the calculation?

It evaluates m_Quotient = h_Index / AcademicAgeYears; HirschProportionality_a = TotalCitations / (h_Index)² (typically 3 ≤ a ≤ 5) directly in your browser and renders three custom SVG charts in real time.

Can I solve backwards for an input parameter using Goal Seek?

Yes. Click "🎯 Goal Seek" in the results toolbar to solve backwards for any numeric input field.

Does this tool work offline?

Yes. All calculations run 100% locally in your browser with full offline PWA support.

Education · Psychometrics & Assessment

Academic Citation Impact (h-Index, m-Quotient, g-Index & Citation Velocity) Calculator: inputs, method, and how to read the result

Analyze scholar citation impact via h-index, career-normalized m-quotient, and Lotka/Hirsch ratio a = Citations/h².

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Current H Index: Author’s current Hirsch h-index (h papers with at least h citations each).
  • Total Career Citations: Total cumulative citations across all published papers.
  • Years Since First Publication: Academic age in years since first peer-reviewed publication.
  • Annual New Citations Velocity: Current annual citation velocity (citations/year).

What the calculation includes

With the default values shown, Hirsch Career-Normalized m-Quotient is 1.8 h / year. The calculation follows Academic h-Index & m-Quotient Formula; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Current H Index from 18 h-index to 20 h-index changes Hirsch Career-Normalized m-Quotient from 1.8 h / year to 2 h / year. This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses official NIST Special Publication 811, IEEE/RFC systems engineering, APA psychometric, and USNO astronomical formulas.
  • Empirical metallurgy and calendar conversions represent standard reference-condition approximations.

Scope: Global NIST, IEEE, APA & Astronomical Standard Check the assumptions and limitations against your situation before relying on the estimate.

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