Losada Ratio (2.9013): Ideal Happiness to Unhappiness Ratio

2.9013 is the minimum ratio of positive to negative emotions we need to experience in our a positive, happy, and flourishing. This number is also called the Losada Ratio, Losada Line, 3-to-1 Ratio, or the Critical Positivity Ratio. It was calculated by Psychologists Barbara Fredrickson and Marcial Losada in their widely cited 2005 paper called Positive affect and the complex dynamics of human flourishing, published in American Psychologist [1].

Losada Ratio = 2.9013

Upon its publication, Losada Ratio received a huge international interest both in academic and general public circles (being cited over 320 times after 8 years of its release [2]), as it provided an easy mathematically proven way to look at our emotions and identify whether we are flourishing or languishing. Fredrickson herself claimed that “the 3-to-1 positivity ratio that will change your life” and that it “may well be a magic number in human psychology” [3].

How 2.9013 Will Change Your Life?

Losada Ratio states that for every 1 negative emotion we need to experience 2.9013 (or simply 3) times more positive emotions in order to be positive and flourishing. Oppositely, if we experience anything less than 2.9013 positive emotions, then this is why we are unhappy and languishing.

Fredrickson and Losada further stated that 2.9013 is the minimal amount of positive emotions we need to have for every negative emotion to feel happy and flourishing. Instead, we should aim at having as much as 11.6346 (12-to-1 ratio) of positive to negative emotion in order to guarantee happiness and flourishing. 

Why Losada Ratio is so Significant?

The significance of the Losada Ratio can’t be overstated. It is a mathematical model that explains why we feel happy and unhappy in an easy and logical way.

For example, we know that the corporate world is notoriously negative and stressful, as people are overwhelmed, overworked, and faced with unreasonable deadlines. In turn, this means that they are receiving more criticism and negative feedback than positive emotions, tilting the positive to negative Losada Ratio below the 2.9013 mark.

Certainly, this is a reason why so many people reporting to be dissatisfied with their jobs. To fix this, employers should give significantly more positive feedback, reduce work-related stress, and create a more positive work environment, in order to push Losada Line over 2.9013.

Similarly, in every other part of our lives, we should strive to be more positive, friendly, and agreeable to make our lives, and these of other fellow human beings, more positive and enjoyable. It is just too easy to be negative and critical. However, despite this ease, we should still try to be more positive than negative. After all, we are trying to create three to twelve times more positive emotions for every negative one.

Criticism of Losada Ratio

To oppose everything stated above, Nicholas Brown, Alan Sokal, and Harris Friedman published a 2013 paper also in American Psychologist [4]. There they discredited Losada Ratio by claiming that there are “numerous fundamental, conceptual, and mathematical errors” with this paper.

Raimo Hämäläinen, Jukka Luoma, and Esa Saarinen further built on this criticism stating that while there were no fundamental errors with math, there were numerous problems in the interpretation and justification of the math used [5]. Finnish researchers stated that “only very limited explanations are given about the modeling process and the meaning and interpretation of its parameters” while “the model also produces strange and previously unreported behavior under certain conditions.”

Fredrickson and Losada agreed with the above criticism choosing to retract their 2.9013 Losada Ratio paper from American Psychologist.

Why We Should Still Believe in the 2.9013 Losada Ratio?

Despite the above criticism, scholars and coaches around the world still believe in Losada Ratio, perhaps not on a purely scientific level, but because it makes sense:

  • Having more positive emotions than the negative ones will make us happier and another way around;
  • We need to make an extra effort to be happy simply because there is so much negativity in our everyday lives;
  • We should avoid unnecessary negativity and force ourselves to find more joy in the everyday moments, sharing this positive energy with other people, to make our life and work more manageable and enjoyable.

Sure, it’s true that we want to be as scientific as possible when it comes to our everyday life, simply because there is so much misinformation spread by politics and media to promote self-interest, while science remains the last refuge of truthfulness, as data never lie.

Still, Losada Line has so much to offer in terms of positive advice, as it is pointing us in the right direction. As such, we genuinely propose people to still try to experience 2.9013 (or more!) positive for every negative emotion, since this level of positivity will certainly make us happy, positive, and flourishing.

We Need to be Even More Positive

Following your feedback on this article, we decided to provide more ideas on how to be more positive in our everyday work and life, just because our life can be rather negative and it can be difficult to reach the 2.9013 Positivity Ratio, not even mentioning the upper limit, 11.6346:

For example, at work, people often behave as if they have to be there doing their work as an obligation and without a single complaint. Respectfully, many people chose stress, complaints, and negative over positivity, refusing to listen to study after study which confirms that positive emotions bring more out of people than negative ones, such as motivation, focus, and creativity.

In other words, a corporate training should focus on improving corporate positivity, by applying lessons of the Losada Ratio and trying to give 2.9013 positive remarks for every single negative one (we know this can be a rather difficult task!):

  1. Complements: people should give more compliments to each other over:

    Work in progress (e.g., you are really doing well on this project!),
    Finished project (e.g., the work you did is fantastic),
    Past projects (e.g., this work you did in the past is really paying off for itself, isn’t it?),
    Being helpful, smart, dedicated, etc.
  2. Saying thank you and welcome: Saying “thank you,” “welcome,” or anything else positive isn’t a sign of weakness as it takes more strength to be positive than negative. As such, it is the strong people who are more positive than their negative counterparts.
  3. Don’t purposefully get on each other’s nerves: Avoiding saying nasty is as much part of the process as being positive. And while often it seems like:

    (1) our well noted criticism should build people up, it does the reverse, which is why,
    (2) knowing when to keep our mouth closed and not say something nasty, and rather
    (3) complimenting people instead of bringing them down,

    is as much of an art as science!
  4. It’s not fake if you practice being genuine: Many people find it difficult to switch from well-established negative patterns to positive ones, but practice makes perfect. So while, at first, it may feel unnatural, fake, and wrong to be overly positive, over time the real you will shine through and your positivity will make your life, and the lives of those around you, more positive and happy overall.

Lastly, despite the criticism Losada Ratio received in scientific circles, we still hope you will continue using its principles in your everyday life, as this theory is wrong does not mean that you should revert back to negative patterns. Rather, you should embrace the positivity ratio and strive to have 2.9013 times more positive emotions for every negative one!


1) Marcial, Losada and Fredrickson, Barbara (2005), “Positive affect and the complex dynamics of human flourishing.” American Psychologist, 60 (7), 678–86. 

2) Bower, Bruce (2013), “Ratio for a Good Life Exposed as ‘Nonsense’“. Science News. Retrieved 2013-08-15.

3) Positivity: Top-Notch Research Reveals the 3-To-1 Ratio That Will Change Your Life by Fredrickson, Barbara. ISBN: 9780307393746.

4) Brown, Nicholas; Sokal, Alan and Friedman Harris (2013), “The complex dynamics of wishful thinking: the critical positivity ratio.” American Psychologist, 68 (9), 801–13. 

5) Hämäläinen, Raimo; Luoma, Jukka; and Saarinen, Esa (2014), “Mathematical modeling is more than fitting equations.”

Roman Russo

Roman Russo

Roman Russo is the visionary founder, senior happiness coach, and Chief Happiness Officer of Optimal Happiness. He has written the revolutionary Optimal Happiness: The Fastest and Surest Way to Reach Your Happiest Potential, a must-read book about achieving our happiest potential. After researching this field for over eight years, Roman is confident that anyone can become happy and invites us to undertake this transformation. Are you ready to start living the life you always meant to live?

3 thoughts on “Losada Ratio (2.9013): Ideal Happiness to Unhappiness Ratio”

  1. I love how you see the positive side of the Losada Line even though we know now that this mathematical theory is scientifically wrong it does make perfect sense and there have been studies that prove that happines is contagious and that positive emotions make us happier! So why not think there’s a tilting point between happy/unhappy people?
    Many of studies are thanks to the Losada Line idea

  2. Dear Eileen, I appreciate your in-depth knowledge of this subject. Indeed, there are many authors who measure happiness by the ratio of happy to unhappy moments. This can be done on a daily, weekly, or lifetime scale. As such, I believe that a good way to see how we are doing in life is how often we are happy / unhappy, and try to maximize these happy moments.

  3. Pingback: Happiness Mathematics: 13 Formulas That Will Make You Happy

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“The problem is that of optimization,” states Roman Russo, author of Optimal Happiness: The Fastest & Surest Way To Reach Your Happiest Potential. Most people will tell you how to be less unhappy or more happy, but no one is speaking about how to be the happiest we can be. And this is the difference that makes all the difference. By not looking at our happiest potential, we fall short of achieving it. After all, we all have hundreds of ideas on how to be happier or less sad, but most people still feel like they are not living their best lives. As such, Optimal Happiness explores the question of how to be the happiest we can be, regardless of who we are, where we are from, and what our life circumstances are. It proposes a complete formula for happiness and explains how to optimize the formula so we can be happy today and forever, breaking down what it really takes to become one of the happiest people alive (spoiler: it isn’t what most people think it is).

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