The Relationship Equation

Why do we stay in relationships that make us unhappy, and why can the same argument mean something completely different to two people?

By Craig Fookes | The Mind Works

I've occasionally had people tell me in the therapy room that they've always thought they were a bit thick because they weren't very good at maths at school. It's quite a lot of baggage to carry from a maths lesson. I was reasonably good at maths. And, to be fair, most of what I learnt has been remarkably useless in my everyday life! Yet something like struggling with maths at school can stay with us for decades.

We can carry around a belief that we're not particularly intelligent, capable or good enough, simply because we struggled with something that somebody else seemed to find easy. It's a good example of something I explored in my previous article about the Nine Conditions for Contentment. Our Sense of Self isn't just about who we are. It's also about what we've come to believe about ourselves. And those beliefs can influence how we experience all sorts of situations, including our relationships.

Which brings me, perhaps rather unexpectedly, back to mathematics. And, rather improbably, I've ended up using algebra to think about relationships.

Now, before anybody starts having uncomfortable flashbacks to their GCSE maths lessons, don't worry.

There won't be a test at the end, I promise.

And you don't need to be good at maths to understand it. In fact, the interesting part isn't really the maths at all. It's the five things we're putting into the equation.

Why do we stay in relationships that make us unhappy?

It's a question that comes up in therapy, in conversations with friends and, let's face it, in our own heads. Sometimes we're talking about a relationship involving frequent arguments, disappointment or a gradual loss of emotional connection. Someone might recognise that they're unhappy. They might feel lonely, unheard or unsupported. They may even have been considering whether the relationship should continue for years.

And yet, the prospect of leaving can feel almost unbearable. From the outside, somebody might wonder why they don't simply end the relationship and move on. But that rather overlooks something important.

We're not just weighing up how unhappy we feel in the relationship. We're also weighing up what we believe life would be like without it. And those are two very different things.

Imagine a set of scales

On one side, we have the emotional cost of remaining in the relationship. On the other, we have the anticipated emotional and practical cost of leaving.

Side A: The burden of remaining in the relationship.

Side B: The anticipated burden of separation.

Both sides are influenced by several factors, and the balance between them may help explain why someone continues to protect a relationship even when it's causing considerable distress. For the purposes of the model, I've identified five factors. Or, because we're pretending to be mathematicians, five numbers.

Side A: What does it feel like to stay?

1. Relationship Conflict (R)

The first number concerns the disagreements, arguments, disappointments and conflicts we experience within a relationship. Some disagreements are relatively minor. Whose turn is it to cook dinner? Why is there always washing left next to the laundry basket rather than actually in it? Why can't somebody simply put their pants in the washing basket? Other disagreements are far more significant. Money, parenting, intimacy, trust, broken promises or feeling that we're carrying too much responsibility.

Relationship conflict represents the emotional impact of these experiences. But here's where things become interesting. Two people can have exactly the same argument and experience it entirely differently.

And the immediate disagreement may be only part of the reason.

2. Disconnection (D)

Imagine having an argument with your partner about something relatively ordinary.

Perhaps they forgot to do something they'd promised. The first time, you might feel mildly annoyed. But what if it's happened repeatedly? What if you've raised the issue many times, explained why it matters, and still feel that nothing changes? The argument may no longer be about the original problem. It may have become about something much more significant. You don't listen to me. You don't understand how I feel. My needs don't matter. I'm carrying all of this on my own. Within the equation, I call this accumulated experience Disconnection.

And I think it can have an amplifying effect. The more disconnected we feel, particularly when previous difficulties haven't been meaningfully resolved, the more emotionally significant the next disagreement may become. A relatively minor argument can begin carrying the weight of many previous experiences.

Of course, this doesn't happen in every relationship or every disagreement. But it may help explain why somebody can become extremely upset about something that appears, on the surface, to be relatively insignificant. It's not necessarily just about what happened today. It's about what today's experience has come to represent.

3. Connection Safety (S)

Now we come to something that can have almost the opposite effect. Our sense of safety within the relationship. Do we feel genuinely loved and valued? Can we disagree without fearing that the relationship itself is under threat? Do we believe our partner cares about our feelings, even when they see things differently? Can we trust that difficulties will be addressed, rather than ignored or repeatedly dismissed? This is what I call Connection Safety. And I think it can make an enormous difference to how we experience conflict. Imagine two couples having a similar disagreement.

In the first relationship, both partners feel secure in their connection. They might get annoyed, disagree quite strongly, or need some time apart. But underneath the disagreement, there's a sense that the relationship is safe. They know they care about one another. They expect to be able to talk things through. And they have sufficient confidence in the relationship that an argument doesn't automatically become a threat to their future together.

Now imagine the same disagreement in a relationship where somebody already feels emotionally disconnected. Perhaps they've spent months feeling unheard. Perhaps previous disagreements have never really been resolved.

Perhaps they're uncertain whether their partner still loves them. The same argument might feel dramatically more threatening. The disagreement hasn't necessarily changed. The emotional context in which it's being experienced has. Within the equation, Connection Safety acts as a buffer. It can reduce the emotional impact of conflict and the accumulated sense of disconnection. Not because disagreements don't matter, but because feeling secure in a relationship can change what those disagreements mean. And importantly, this safety needs to be experienced, rather than simply assumed. Being told that somebody loves us isn't always the same as feeling loved, understood and secure with them.

Side B: What do we believe will happen if we leave?

The other side of the scales concerns the anticipated consequences of separation. And here we have two further numbers.

4. Anticipated Loneliness (L)

What would life feel like without this person? It's a question that can carry enormous emotional weight. For some people, separation represents the loss of companionship, affection, intimacy and the person they share their everyday lives with. They may worry about waking up alone. Having nobody to talk to at the end of the day. Losing the person who knows their history, routines and vulnerabilities. Or losing the future they'd imagined together. For others, the prospect of separation may activate much deeper worries. What if nobody else wants me? What if this is my only chance of being loved?

What if I can't cope on my own? What if I end up alone forever? These feelings can be extraordinarily powerful. And here's something worth considering. The loneliness we anticipate after leaving a relationship isn't necessarily the same as the loneliness we'd actually experience.

We're making a prediction. And that prediction may be influenced by our experiences, our beliefs about ourselves, our confidence, our available support and the circumstances we're living within. Someone may be deeply unhappy in a relationship yet imagine that being without it would feel considerably worse. That anticipated loneliness can become a powerful reason to preserve the relationship.

5. Separation Impact (I)

Of course, ending a relationship isn't simply an emotional decision. There are practical consequences too.

Where would we live? Could we afford to manage financially? What would happen with the children? Would we lose contact with shared friends or family? How would our routines, responsibilities and everyday lives change? Would we lose practical support that we depend upon?

These considerations can be especially significant when someone has limited financial resources, caring responsibilities, health difficulties or relatively little support outside the relationship. Within the model, I call this Separation Impact. And it may amplify the emotional burden we anticipate.

For example, being worried about loneliness is one thing. Being worried about loneliness while also facing financial insecurity, housing difficulties and the loss of familiar support is quite another.

The practical consequences can make an already difficult emotional decision feel considerably more threatening. This is why it's important not to assume that somebody remains in an unhappy relationship simply because they lack confidence or are frightened of being alone. Sometimes the circumstances really are difficult.

So, what's the actual equation?

Right, here comes the maths. Remember our two sets of scales? We have three numbers on Side A: Relationship Conflict (R) Disconnection (D) Connection Safety (S) And two on Side B: Anticipated Loneliness (L) Separation Impact (I) Here's how I've brought them together. Side A: Relational Burden

A = [R × (1 + D)] ÷ (1 + S)

Side B: Anticipated Separation Burden

B = L × (1 + I)

And the relationship between them is expressed as:

A < B

Or, in plain English: When the anticipated emotional and practical burden of leaving feels greater than the distress of remaining, staying may feel like the less threatening option.

That's it. All those maths lessons, and we've arrived at the possibility that people tend to protect themselves from whichever situation they believe will hurt more. Who knew algebra could be useful after all? But there are two particularly interesting things happening within those calculations.

First, Disconnection amplifies the impact of conflict, while Connection Safety reduces it. Second, Separation Impact amplifies Anticipated Loneliness. So we might have two relationships experiencing similar levels of conflict, but with very different emotional consequences.

And we might have two people considering separation, but anticipating entirely different experiences of life afterwards. The numbers are a way of illustrating those relationships. They're not established clinical measurements, and the equation isn't a calculator that can tell us whether somebody should stay or leave. The useful part is the way it encourages us to consider all five factors, rather than assuming relationship decisions are straightforward.

Why can two people experience the same relationship so differently?

Here's the complication: there are two people in a relationship, and they're not necessarily standing on the same set of scales. We often assume that if two people experience the same event, they'll have broadly similar feelings about it. But that's rarely how human relationships work. We all bring our own histories, expectations, insecurities, experiences and beliefs into our relationships. And these can influence how we interpret what happens.

You may have come across discussions about attachment styles, particularly online, where anxious and avoidant attachment have become increasingly familiar terms. Attachment theory offers some useful ways of understanding how people experience closeness, dependence, rejection and emotional safety.

But I think we need to be careful about turning these tendencies into fixed identities. You don't suddenly become an 'anxious' or 'avoidant' person because a video on your phone tells you so.

Someone with more anxious attachment tendencies

Imagine someone who has a relatively negative view of themselves but tends to see other people as sources of safety, reassurance or emotional security. They may feel a particularly strong need to preserve a close relationship.

Even when the relationship becomes difficult, the connection itself may represent something they desperately want to protect. Arguments might feel threatening because they raise the possibility of rejection or abandonment. And the anticipated loneliness associated with separation may feel almost intolerable. Within our equation, Side B may become extremely heavy. The anticipated consequences of leaving can outweigh considerable distress within the relationship.

This doesn't mean the person is irrational, dependent or incapable of making decisions. It means that their experience of the relationship, and their expectations about losing it, may place considerable emotional weight on preserving the connection.

Someone with more avoidant attachment tendencies

Now imagine someone who experiences emotional closeness or dependence rather differently. They may value their independence strongly. They might find emotional demands uncomfortable or experience repeated relationship conflict as a threat to their autonomy.

As disconnection or pressure increases, the relationship may begin to feel less safe or less rewarding. And when they imagine separation, they may anticipate relief rather than overwhelming loneliness. The prospect of having their own space, fewer emotional demands and greater independence may seem appealing. Within the equation, Side A may feel considerably heavier than Side B. The burden of remaining can outweigh the anticipated consequences of leaving.

Again, this doesn't mean someone with avoidant tendencies doesn't love their partner or won't experience grief or loneliness following separation. It simply illustrates how different expectations about closeness, safety and loss may influence the balance.

And of course, these patterns aren't fixed. The same person can respond differently depending on the relationship, their current circumstances, their health and how much emotional capacity they have available.

What happens when the scales change?

One of the things I particularly like about this model is that the balance isn't necessarily permanent. The five factors can change over time. A couple may experience frequent disagreements but develop better ways of understanding and repairing them. That may reduce accumulated disconnection and strengthen Connection Safety. Someone who previously feared separation may develop stronger friendships, greater financial independence or more confidence in their ability to cope. Their anticipated loneliness and separation impact may begin to feel different. Equally, continuing conflict, declining trust or increasing practical pressures may gradually change the balance in the other direction.

This means that a person's willingness to remain in or leave a relationship may change even when the broad circumstances appear relatively similar. And it also helps explain why the decision that feels possible today may have felt completely impossible a year ago.

Does this mean we should stay until the scales tip?

Absolutely not. This is an explanatory model, rather than a guide to relationship decisions. It doesn't tell us whether a relationship is healthy, whether someone should stay or whether leaving would be the right decision. And it's particularly important to recognise that abusive, controlling or dangerous relationships require consideration of safety, rather than a mathematical comparison of emotional costs.

There may also be circumstances where somebody stays for reasons involving responsibilities, values, commitments or choices that aren't adequately represented by these five factors. The equation is deliberately simplified. Its purpose is to help us explore why certain decisions or emotional responses may make sense from the person's perspective.

Because when we understand the different pressures and expectations involved, we may be better able to recognise what needs attention. Sometimes that means improving communication and rebuilding trust. Sometimes it means strengthening support or addressing practical difficulties. And sometimes it involves recognising that a relationship can no longer provide the safety, connection or quality of life that somebody needs.

What does this tell us about contentment?

In my previous article, I introduced the Nine Conditions for Contentment, organised around Connection, Resources and Identity. I think the Relationship Equation provides a particularly useful example of how these three areas interact.

Connection: Do we feel seen, heard, held and emotionally safe within the relationship? What connection do we anticipate losing?

Resources: What time, energy, money, practical support and opportunities would be affected by remaining or separating? Identity: What have we come to believe about ourselves, our worth, our ability to cope and what the relationship means about who we are? A relationship decision can involve all three simultaneously.

And perhaps that's why something that looks straightforward from the outside can feel so complicated when we're the person living through it. The central question isn't simply whether we love somebody or whether we argue too much.

It's also about what the relationship provides, what it costs, what we expect would happen without it, and what those experiences mean to us. That's what I've been trying to explore through the Relationship Equation. Not to reduce human relationships to five numbers. But to use five numbers to help us think a little more clearly about something that can be extraordinarily complicated.

And perhaps, after all these years, I've finally found a use for some of that maths I learnt at school.

Craig Fookes

Clinical Hypnotherapist | Founder of The Mind Works

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